Problem:
Mary chose an even 4-digit number . She wrote down all the divisors of in increasing order from left to right: . At some moment Mary wrote 323 as a divisor of . What is the smallest possible value of the next divisor written to the right of 323 ?
Answer Choices:
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Solution:
Let be the next divisor of after 323. Then , because otherwise , contrary to the fact that is a 4 -digit number. Therefore . The prime factorization of 323 is . Thus the next divisor of is at least . Indeed, will be the next number in Mary's list when .
The problems on this page are the property of the MAA's American Mathematics Competitions