{"id":3857,"date":"2023-09-15T14:26:00","date_gmt":"2023-09-15T18:26:00","guid":{"rendered":"http:\/\/mathfun4kids.com\/mlog\/?p=3857"},"modified":"2024-10-25T09:44:27","modified_gmt":"2024-10-25T13:44:27","slug":"mathcounts-training-number-theory-5","status":"publish","type":"post","link":"https:\/\/mathfun4kids.com\/mlog\/?p=3857","title":{"rendered":"MathCounts Training &#8211; Number Theory &#8211; 5"},"content":{"rendered":"\n<ol><li>________ Let $(a\\times b\\times c)\\div(a+b+c)=341$ to be an equation where $a$, $b$ and $c$ are consecutive positive integers. What is the least possible value of $a$? $$ $$<\/li><li>________ The letters $A$, $B$, $C$, $D$, $E$ and $F$ represent digits and $ABC,DEF$ represents a positive six-dight integer. What is the number $ABC,DEF$ if $$4(ABC,DEF)=3(DEF,ABC)$$ $$ $$<\/li><li>________ Jan is thinking of a positive integer. Her integer has exactly 16 positive divisors, two of which are 12 and 15. What is Jan&#8217;s number? $$ $$<\/li><li>________ Mady has an infinite number of balls and empty boxes available to her. The empty boxes, each capable of holding four balls, are arranged in a row from left to right. At the first step, she places a ball in the first box (the leftmost box) of the row. At each subsequent step, she places a ball in the first box of the row that still has room for a ball and empties any boxes to its left. How many balls in total are in the boxes as a result of Mady&#8217;s $2010^{th}$ step? $$ $$<\/li><li>________ The product of a set of positive integers is 144. What is the least possible sum of this set of positive integers? $$ $$<\/li><\/ol>\n","protected":false},"excerpt":{"rendered":"<p>________ Let $(a\\times b\\times c)\\div(a+b+c)=341$ to be an equation where $a$, $b$ and $c$ are consecutive positive integers. What is the least possible value of $a$? $$ $$ ________ The letters $A$, $B$, $C$, $D$, $E$ and $F$ represent digits &hellip; <a href=\"https:\/\/mathfun4kids.com\/mlog\/?p=3857\">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":[18,11,16],"tags":[],"_links":{"self":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3857"}],"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=3857"}],"version-history":[{"count":4,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3857\/revisions"}],"predecessor-version":[{"id":3861,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3857\/revisions\/3861"}],"wp:attachment":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3857"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3857"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3857"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}