{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-16T00:20:21.000Z","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":"2026-05-16T00:00:00.000Z","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":44071,"title":"Smallest n, for n! to have m trailing zero digits","description":"For given positive integer n, its factorial often has many trailing zeros, in other words many factors of 10s. In order for n! to have at least \"m\" trailing zeros, what is the smallest \"n\" ?\r\nExample: factorial(10) = 3628800 factorial(9) = 362880 In order to have 2 trailing zeros on factorial, the smallest n is 10.\r\nOptional: Can you make an efficient algorithm for a very large m?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 102px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 51px; transform-origin: 407px 51px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.5px 8px; transform-origin: 378.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor given positive integer n, its factorial often has many trailing zeros, in other words many factors of 10s. In order for n! to have at least \"m\" trailing zeros, what is the smallest \"n\" ?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376px 8px; transform-origin: 376px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample: factorial(10) = 3628800 factorial(9) = 362880 In order to have 2 trailing zeros on factorial, the smallest n is 10.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 205px 8px; transform-origin: 205px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOptional: Can you make an efficient algorithm for a very large m?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = factorialForZeros(m)\r\n  n = 1000;\r\nend","test_suite":"%%\r\nfiletext = fileread('factorialForZeros.m');\r\nillegal = contains(filetext, 'str2num') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'switch') || contains(filetext, 'elseif'); \r\nassert(~illegal)\r\n\r\n%%\r\nm = 1;\r\nn_correct = 5;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n\r\n%%\r\nm = 2;\r\nn_correct = 10;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n\r\n%%\r\nm = 6;\r\nn_correct = 25;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n\r\n%%\r\nm = 5;\r\nn_correct = 25;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n\r\n%%\r\nm = 4;\r\nn_correct = 20;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n \r\n%%\r\nm = 156;\r\nn_correct = 625;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n\r\n%%\r\nm = 155;\r\nn_correct = 625;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n \r\n%%\r\nm = 154;\r\nn_correct = 625;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n\r\n%%\r\nm = 153;\r\nn_correct = 625;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n\r\n%%\r\nm = 152;\r\nn_correct = 620;\r\nassert(isequal(factorialForZeros(m),n_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":115733,"edited_by":223089,"edited_at":"2023-01-07T09:00:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":61,"test_suite_updated_at":"2023-01-07T09:00:18.000Z","rescore_all_solutions":false,"group_id":673,"created_at":"2017-02-14T01:10:18.000Z","updated_at":"2026-03-20T13:48:37.000Z","published_at":"2017-02-14T01:10:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor given positive integer n, its factorial often has many trailing zeros, in other words many factors of 10s. In order for n! to have at least \\\"m\\\" trailing zeros, what is the smallest \\\"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\u003eExample: factorial(10) = 3628800 factorial(9) = 362880 In order to have 2 trailing zeros on factorial, the smallest n is 10.\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\u003eOptional: Can you make an efficient algorithm for a very large m?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":44071,"title":"Smallest n, for n! to have m trailing zero digits","description":"For given positive integer n, its factorial often has many trailing zeros, in other words many factors of 10s. In order for n! to have at least \"m\" trailing zeros, what is the smallest \"n\" ?\r\nExample: factorial(10) = 3628800 factorial(9) = 362880 In order to have 2 trailing zeros on factorial, the smallest n is 10.\r\nOptional: Can you make an efficient algorithm for a very large m?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 102px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 51px; transform-origin: 407px 51px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.5px 8px; transform-origin: 378.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor given positive integer n, its factorial often has many trailing zeros, in other words many factors of 10s. In order for n! to have at least \"m\" trailing zeros, what is the smallest \"n\" ?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376px 8px; transform-origin: 376px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample: factorial(10) = 3628800 factorial(9) = 362880 In order to have 2 trailing zeros on factorial, the smallest n is 10.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 205px 8px; transform-origin: 205px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOptional: Can you make an efficient algorithm for a very large m?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = factorialForZeros(m)\r\n  n = 1000;\r\nend","test_suite":"%%\r\nfiletext = fileread('factorialForZeros.m');\r\nillegal = contains(filetext, 'str2num') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'switch') || contains(filetext, 'elseif'); \r\nassert(~illegal)\r\n\r\n%%\r\nm = 1;\r\nn_correct = 5;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n\r\n%%\r\nm = 2;\r\nn_correct = 10;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n\r\n%%\r\nm = 6;\r\nn_correct = 25;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n\r\n%%\r\nm = 5;\r\nn_correct = 25;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n\r\n%%\r\nm = 4;\r\nn_correct = 20;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n \r\n%%\r\nm = 156;\r\nn_correct = 625;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n\r\n%%\r\nm = 155;\r\nn_correct = 625;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n \r\n%%\r\nm = 154;\r\nn_correct = 625;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n\r\n%%\r\nm = 153;\r\nn_correct = 625;\r\nassert(isequal(factorialForZeros(m),n_correct))\r\n\r\n%%\r\nm = 152;\r\nn_correct = 620;\r\nassert(isequal(factorialForZeros(m),n_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":115733,"edited_by":223089,"edited_at":"2023-01-07T09:00:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":61,"test_suite_updated_at":"2023-01-07T09:00:18.000Z","rescore_all_solutions":false,"group_id":673,"created_at":"2017-02-14T01:10:18.000Z","updated_at":"2026-03-20T13:48:37.000Z","published_at":"2017-02-14T01:10:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor given positive integer n, its factorial often has many trailing zeros, in other words many factors of 10s. In order for n! to have at least \\\"m\\\" trailing zeros, what is the smallest \\\"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\u003eExample: factorial(10) = 3628800 factorial(9) = 362880 In order to have 2 trailing zeros on factorial, the smallest n is 10.\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\u003eOptional: Can you make an efficient algorithm for a very large 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