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# number theory

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When 310 is divided by a two-digit positive integer K, the remainder is 37. What is the largest possible value of K?

Apr 19, 2021

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$$310 \equiv 37 \pmod {K}$$

$$310-37 \equiv 273 \equiv 0 \pmod K$$

Factor of 273 : 1, 3, 7, 13, 21, 39, 91, 273

Largest possible two-digit positive integer K is 91

Apr 19, 2021