BTGmoderatorDC wrote:If n is an integer and n^3 is divisible by 24, what is the largest number that must be a factor of n?
(A) 1
(B) 2
(C) 6
(D) 8
(E) 12
OA C
Source: Manhattan Prep
Let's factorize 24. We see that 24 = 2^3*3; thus, for n^3 to be divisible by 24 = 2^3*3, n must be a factor of 2 and 3. Orn must be at least 2*3 = 6. So with n =6, we have n^3 = 6^3 = (2*3)^3 = 2^3*3^3, divisible by 24.
Thus, the largest number that must be a factor of n is 6.
The correct answer:
C
Hope this helps!
-Jay
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