Problem Solving (PS) | Re: If p is the product of integers from 1 to 15, what is the greatest

We have to find the greatest possible value of integer k such that:

p/3^k = 15!/3^k = integer

The expression above is an integer if k is not greater than the total number of 3s in the prime factored form of 15!.

We can quickly determine the total number of 3s in 15! with the following technique:

15/3 = 5

5/3 = 1 [Ignore the remainder.]

The total number of 3s is 5 + 1 = 6, so it must be true that:

k ≤ 6

The maximum value of integer k is 6.

Answer: C

Statistics : Posted by JeffTargetTestPrep • on 05 Oct 2023, 01:30 • Replies 2 • Views 259

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