Question

The product 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 is divisible by

(A) 2^11
(B) 2^10
(C) 2^9
(D) 2^8
(E) 2^7

I know the answer but can someone explain a more efficient and quick way to find it?

Answer 1

I would write out the PRIME FACTORIZATION of each number.
Count how many TWO's are in the prime factorization.
There are 7.
So the answer is LETTER E 2^7
5 = 5* 1
6 = 2 * 3
7 = 7 * 1
8 = 2 * 2 * 2
9 = 3 * 3
10 = 2 *5
11 = 11 * 1
12 = 2 * 2 * 3