X is the product of integers from 1 to 10, inclusive. If 2 ^ N is a fa

Question

X is the product of integers from 1 to 10, inclusive. If 2^ N is a factor of X, what is the greatest possible value of N?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

gmatophobia · Answer

The question wants us to find the maximum power of 2 in 10!

We can use successive division to find the same.

10 / 2 = 5

5 / 2 = 2

2 / 2 = 1

Sum of powers = 5 + 2 + 1 = 8

Option C

ninjaintraining · Answer

The prime factorization of 1*2*3*4*5*6*7*8*9*10 yields 8 2s. Therefore, 2^8 is the largest possible factor.  Answer C.

Paras96 · Answer

For deriving the power of a prime no. "X" in the factorial of a no. "N", successive division with only quotient has to be done repetitively with divisor as X until we get 1. For the answer, add the respective quotient.

Here,
10/2=5
5/2=2
2/2=1

Therefore answer = 5+2+1=8

Here,
10/2=5
5/2=2
2/2=1

Therefore answer = 5+2+1=8

bumpbot · Answer

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X is the product of integers from 1 to 10, inclusive. If 2 ^ N is a fa

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X is the product of integers from 1 to 10, inclusive. If 2 ^ N is a fa

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