{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":44782,"title":"Highest powers in factorials","description":"This is the inverse of the problem \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44747 Exponents in Factorials\u003e.  Instead of being given a number and finding out the highest exponent it can be raised to for a given factorial, you'll be given a power, and you're being asked to find the highest number that can be raised to that power for a given factorial.\r\n\r\nFor example, n=7 and p=2.  The highest perfect square (p=2) that can evenly divide 5040 (n=7, and 7!=5040) is 144, or 12^2.  Therefore, your output should be y=12.\r\n\r\nAs before, you can assume that both n and power are integers greater than 1.","description_html":"\u003cp\u003eThis is the inverse of the problem \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44747\"\u003eExponents in Factorials\u003c/a\u003e.  Instead of being given a number and finding out the highest exponent it can be raised to for a given factorial, you'll be given a power, and you're being asked to find the highest number that can be raised to that power for a given factorial.\u003c/p\u003e\u003cp\u003eFor example, n=7 and p=2.  The highest perfect square (p=2) that can evenly divide 5040 (n=7, and 7!=5040) is 144, or 12^2.  Therefore, your output should be y=12.\u003c/p\u003e\u003cp\u003eAs before, you can assume that both n and power are integers greater than 1.\u003c/p\u003e","function_template":"function y = biggest_power(n,p)\r\n  y = n*p;\r\nend","test_suite":"%%\r\nn=7;p=2;y=biggest_power(n,p)\r\nassert(isequal(y,12));\r\n%%\r\nn=30;p=4;y=biggest_power(n,p)\r\nassert(isequal(y,60480));\r\n%%\r\nn=25;p=11;y=biggest_power(n,p)\r\nassert(isequal(y,4));\r\n%%\r\nn=1000;p=100;y=biggest_power(n,p)\r\nassert(isequal(y,7257600));\r\n%%\r\ns=0;\r\np=10;\r\nfor n=100:-1:20\r\n    s(n-19)=biggest_power(n,p);\r\nend\r\nassert(isequal(sum(s),79641800));\r\nassert(isequal(numel(unique(s)),13));\r\nassert(isequal(floor(mean(s)),983232));\r\n%%\r\nn=100;\r\ns=0;\r\nfor p=30:-1:10\r\n    s(p-9)=biggest_power(n,p);\r\nend\r\nassert(isequal(sum(s),14825664));\r\nassert(isequal(numel(unique(s)),7));\r\nassert(isequal(floor(mean(s)),705984));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":71,"created_at":"2018-11-08T14:45:39.000Z","updated_at":"2025-12-14T23:05:05.000Z","published_at":"2018-11-08T14:45:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the inverse of the problem\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44747\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eExponents in Factorials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Instead of being given a number and finding out the highest exponent it can be raised to for a given factorial, you'll be given a power, and you're being asked to find the highest number that can be raised to that power for a given factorial.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, n=7 and p=2. The highest perfect square (p=2) that can evenly divide 5040 (n=7, and 7!=5040) is 144, or 12^2. Therefore, your output should be y=12.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs before, you can assume that both n and power are integers greater than 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44747,"title":"Exponents in Factorials","description":"It's time to get excited about numbers!!!  Well, we're just dealing with factorials here, but it's still a good reason to get excited.  You're given two numbers, n and k.  Calculate the highest exponent of k that could appear in n!\r\n\r\nFor example, for n=5 and k=2, you're looking for the highest exponent of 2 that could appear in 5!, or 120.  The highest power of 2 that evenly divides 120 is 3 (2^3 evenly divides 120, while 2^4 does not) so your output for maxexp(5,2)=3.\r\n\r\nYou can assume that both n and k are both integers greater than 1.\r\n","description_html":"\u003cp\u003eIt's time to get excited about numbers!!!  Well, we're just dealing with factorials here, but it's still a good reason to get excited.  You're given two numbers, n and k.  Calculate the highest exponent of k that could appear in n!\u003c/p\u003e\u003cp\u003eFor example, for n=5 and k=2, you're looking for the highest exponent of 2 that could appear in 5!, or 120.  The highest power of 2 that evenly divides 120 is 3 (2^3 evenly divides 120, while 2^4 does not) so your output for maxexp(5,2)=3.\u003c/p\u003e\u003cp\u003eYou can assume that both n and k are both integers greater than 1.\u003c/p\u003e","function_template":"function y = maxexp(n,k)\r\n\r\n% Maximum exponent of k that can be found in n!\r\n\r\n  y = n-k;\r\nend","test_suite":"%%\r\nassert(isequal(maxexp(5,2),3))\r\n%%\r\nassert(isequal(maxexp(9,3),4))\r\n%%\r\nassert(isequal(maxexp(10,14),1))\r\n%%\r\nq=arrayfun(@(x) maxexp(x,13),2:12);\r\nassert(all(q==0))\r\n%%\r\nassert(isequal(maxexp(67,2),64))\r\n%%\r\nassert(isequal(maxexp(10,4),4))\r\n%%\r\ns1=maxexp(100,3);\r\ns2=maxexp(200,5);\r\nassert(isequal(maxexp(s2,s1)-maxexp(s1,s2),maxexp(100,13)+1))\r\n%%\r\nv=zeros(1,99);\r\nfor a=2:100\r\n    v(a-1)=maxexp(100,a);\r\nend\r\nassert(isequal(sum(v==1),10))\r\nassert(isequal(sum(find(v==2)),496))\r\nassert(isequal(sum(v),1299))\r\nassert(isequal(max(v)-min(v),96))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":2,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":71,"created_at":"2018-10-22T17:29:48.000Z","updated_at":"2025-12-14T23:07:11.000Z","published_at":"2018-10-22T17:29:48.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt's time to get excited about numbers!!! Well, we're just dealing with factorials here, but it's still a good reason to get excited. You're given two numbers, n and k. Calculate the highest exponent of k that could appear in n!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, for n=5 and k=2, you're looking for the highest exponent of 2 that could appear in 5!, or 120. The highest power of 2 that evenly divides 120 is 3 (2^3 evenly divides 120, while 2^4 does not) so your output for maxexp(5,2)=3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou can assume that both n and k are both integers greater than 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":44782,"title":"Highest powers in factorials","description":"This is the inverse of the problem \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44747 Exponents in Factorials\u003e.  Instead of being given a number and finding out the highest exponent it can be raised to for a given factorial, you'll be given a power, and you're being asked to find the highest number that can be raised to that power for a given factorial.\r\n\r\nFor example, n=7 and p=2.  The highest perfect square (p=2) that can evenly divide 5040 (n=7, and 7!=5040) is 144, or 12^2.  Therefore, your output should be y=12.\r\n\r\nAs before, you can assume that both n and power are integers greater than 1.","description_html":"\u003cp\u003eThis is the inverse of the problem \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44747\"\u003eExponents in Factorials\u003c/a\u003e.  Instead of being given a number and finding out the highest exponent it can be raised to for a given factorial, you'll be given a power, and you're being asked to find the highest number that can be raised to that power for a given factorial.\u003c/p\u003e\u003cp\u003eFor example, n=7 and p=2.  The highest perfect square (p=2) that can evenly divide 5040 (n=7, and 7!=5040) is 144, or 12^2.  Therefore, your output should be y=12.\u003c/p\u003e\u003cp\u003eAs before, you can assume that both n and power are integers greater than 1.\u003c/p\u003e","function_template":"function y = biggest_power(n,p)\r\n  y = n*p;\r\nend","test_suite":"%%\r\nn=7;p=2;y=biggest_power(n,p)\r\nassert(isequal(y,12));\r\n%%\r\nn=30;p=4;y=biggest_power(n,p)\r\nassert(isequal(y,60480));\r\n%%\r\nn=25;p=11;y=biggest_power(n,p)\r\nassert(isequal(y,4));\r\n%%\r\nn=1000;p=100;y=biggest_power(n,p)\r\nassert(isequal(y,7257600));\r\n%%\r\ns=0;\r\np=10;\r\nfor n=100:-1:20\r\n    s(n-19)=biggest_power(n,p);\r\nend\r\nassert(isequal(sum(s),79641800));\r\nassert(isequal(numel(unique(s)),13));\r\nassert(isequal(floor(mean(s)),983232));\r\n%%\r\nn=100;\r\ns=0;\r\nfor p=30:-1:10\r\n    s(p-9)=biggest_power(n,p);\r\nend\r\nassert(isequal(sum(s),14825664));\r\nassert(isequal(numel(unique(s)),7));\r\nassert(isequal(floor(mean(s)),705984));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":71,"created_at":"2018-11-08T14:45:39.000Z","updated_at":"2025-12-14T23:05:05.000Z","published_at":"2018-11-08T14:45:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the inverse of the problem\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44747\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eExponents in Factorials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Instead of being given a number and finding out the highest exponent it can be raised to for a given factorial, you'll be given a power, and you're being asked to find the highest number that can be raised to that power for a given factorial.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, n=7 and p=2. The highest perfect square (p=2) that can evenly divide 5040 (n=7, and 7!=5040) is 144, or 12^2. Therefore, your output should be y=12.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs before, you can assume that both n and power are integers greater than 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44747,"title":"Exponents in Factorials","description":"It's time to get excited about numbers!!!  Well, we're just dealing with factorials here, but it's still a good reason to get excited.  You're given two numbers, n and k.  Calculate the highest exponent of k that could appear in n!\r\n\r\nFor example, for n=5 and k=2, you're looking for the highest exponent of 2 that could appear in 5!, or 120.  The highest power of 2 that evenly divides 120 is 3 (2^3 evenly divides 120, while 2^4 does not) so your output for maxexp(5,2)=3.\r\n\r\nYou can assume that both n and k are both integers greater than 1.\r\n","description_html":"\u003cp\u003eIt's time to get excited about numbers!!!  Well, we're just dealing with factorials here, but it's still a good reason to get excited.  You're given two numbers, n and k.  Calculate the highest exponent of k that could appear in n!\u003c/p\u003e\u003cp\u003eFor example, for n=5 and k=2, you're looking for the highest exponent of 2 that could appear in 5!, or 120.  The highest power of 2 that evenly divides 120 is 3 (2^3 evenly divides 120, while 2^4 does not) so your output for maxexp(5,2)=3.\u003c/p\u003e\u003cp\u003eYou can assume that both n and k are both integers greater than 1.\u003c/p\u003e","function_template":"function y = maxexp(n,k)\r\n\r\n% Maximum exponent of k that can be found in n!\r\n\r\n  y = n-k;\r\nend","test_suite":"%%\r\nassert(isequal(maxexp(5,2),3))\r\n%%\r\nassert(isequal(maxexp(9,3),4))\r\n%%\r\nassert(isequal(maxexp(10,14),1))\r\n%%\r\nq=arrayfun(@(x) maxexp(x,13),2:12);\r\nassert(all(q==0))\r\n%%\r\nassert(isequal(maxexp(67,2),64))\r\n%%\r\nassert(isequal(maxexp(10,4),4))\r\n%%\r\ns1=maxexp(100,3);\r\ns2=maxexp(200,5);\r\nassert(isequal(maxexp(s2,s1)-maxexp(s1,s2),maxexp(100,13)+1))\r\n%%\r\nv=zeros(1,99);\r\nfor a=2:100\r\n    v(a-1)=maxexp(100,a);\r\nend\r\nassert(isequal(sum(v==1),10))\r\nassert(isequal(sum(find(v==2)),496))\r\nassert(isequal(sum(v),1299))\r\nassert(isequal(max(v)-min(v),96))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":2,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":71,"created_at":"2018-10-22T17:29:48.000Z","updated_at":"2025-12-14T23:07:11.000Z","published_at":"2018-10-22T17:29:48.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt's time to get excited about numbers!!! Well, we're just dealing with factorials here, but it's still a good reason to get excited. You're given two numbers, n and k. Calculate the highest exponent of k that could appear in n!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, for n=5 and k=2, you're looking for the highest exponent of 2 that could appear in 5!, or 120. 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