Question

If n is a positive integer, which of following statement is individually sufficient to prove whether 289 is a factor of n?a. The greatest common divisor of n and 344 is 86. b. Least common multiple of n and 272 is 4624. c. The least common multiple of n and 289 is 289n.

Answer 1

The statement b) is individually sufficient to prove than 289 is a factor of n

Explanation:

The least common multiple of n and 272 is the smallest number that is a multiple of n and a multiple of 272. Therefore:

272 x X = 4624 ⇒ X = 17 but 272 = 17 · 16 and 289 = 17 · 17

Therefore 17·17 must be a factor of n. That means 289 is a factor of n