Difference between revisions of "2018 AMC 10B Problems/Problem 21"
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Mary chose an even <math>4</math>-digit number <math>n</math>. She wrote down all the divisors of <math>n</math> in increasing order from left to right: <math>1,2,...,\dfrac{n}{2},n</math>. At some moment Mary wrote <math>323</math> as a divisor of <math>n</math>. What is the smallest possible value of the next divisor written to the right of <math>323</math>. | Mary chose an even <math>4</math>-digit number <math>n</math>. She wrote down all the divisors of <math>n</math> in increasing order from left to right: <math>1,2,...,\dfrac{n}{2},n</math>. At some moment Mary wrote <math>323</math> as a divisor of <math>n</math>. What is the smallest possible value of the next divisor written to the right of <math>323</math>. | ||
<math>\textbf{(A) } 324 \qquad \textbf{(B) } 330 \qquad \textbf{(C) } 340 \qquad \textbf{(D) } 361 \qquad \textbf{(E) } 646</math> | <math>\textbf{(A) } 324 \qquad \textbf{(B) } 330 \qquad \textbf{(C) } 340 \qquad \textbf{(D) } 361 \qquad \textbf{(E) } 646</math> | ||
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| + | ==Solution== | ||
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| + | ==See Also== | ||
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| + | {{MAA Notice}} | ||
Revision as of 15:32, 16 February 2018
Problem
Mary chose an even 
-digit number 
. She wrote down all the divisors of in increasing order from left to right: 
. At some moment Mary wrote 
as a divisor of . What is the smallest possible value of the next divisor written to the right of .
Solution
See Also
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
