{"id":3862,"date":"2023-09-22T21:32:00","date_gmt":"2023-09-23T01:32:00","guid":{"rendered":"http:\/\/mathfun4kids.com\/mlog\/?p=3862"},"modified":"2024-10-25T09:45:03","modified_gmt":"2024-10-25T13:45:03","slug":"mathcounts-training-number-theory-6","status":"publish","type":"post","link":"https:\/\/mathfun4kids.com\/mlog\/?p=3862","title":{"rendered":"MathCounts Training &#8211; Number Theory &#8211; 6"},"content":{"rendered":"\n<ol><li>________ What is the sum of all positive two-digit integers with exactly 12 positive factors? $$ $$<\/li><li>________ What is the sum of the three numbers less than 1000 that have exactly five positive  integer divisors? $$ $$<\/li><li>________ The sequence 3, 4, 13, 15, 30, 33, 54, 58, 85, 90, &#8230;. contains, in increasing order, all the positive integers that yield a triangle number when multiplied by 7. What is the $100^{th}$ term of this sequence? $$ $$<\/li><li>________ How many whole numbers $n$, such that $100 \\le n \\le 1000$, have the same number of odd factors as even factors? $$ $$<\/li><li>________ How many positive integer factors of $2020$ have more than $3$ factors? (As an example, $12$ has $6$ factors, namely $1,2,3,4,6,$ and $12$.$$ $$<\/li><\/ol>\n","protected":false},"excerpt":{"rendered":"<p>________ What is the sum of all positive two-digit integers with exactly 12 positive factors? $$ $$ ________ What is the sum of the three numbers less than 1000 that have exactly five positive integer divisors? $$ $$ ________ The &hellip; <a href=\"https:\/\/mathfun4kids.com\/mlog\/?p=3862\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[13,18,11],"tags":[],"_links":{"self":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3862"}],"collection":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3862"}],"version-history":[{"count":5,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3862\/revisions"}],"predecessor-version":[{"id":4580,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3862\/revisions\/4580"}],"wp:attachment":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3862"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3862"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3862"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}