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题库 / Prep2007E1-DS-170
If n and t are positive integers, what is the greatest prime factor of the product nt ?
(1) The greatest common factor of n and t is 5.
(2) The least common multiple of n and t is 105.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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“（1）即n=5a, t=5b, 问nt即25ab的最大质因数，但a或b都可以是比5大的质因数，比如7/11等，所以无法确定nt最大质因数； (2) n,t 只可能是3,5，7之一或二者或三者相乘，最大不超过105=3*5*7, （n或者t如果有一个超过了105， 那最小公倍数就不会是105），所以nt相乘最大的质因数就是7”
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