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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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n、t都是正整数，问nt乘积的最大质因子。
n和 t的最大公因子是5
n、t的最小公倍数是105
如果n=5,t=70，最大质因子为7；如果n=5,t=15，最大质因子为5，所以条件1不充分
因为最小公倍数是105，7和15唯一符合条件，最大质因子是7，条件2充分
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