If m is the product of all integers from 1 to 40, inclusive, what is the greatest integer p for which 10^p is a factor of m?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
OA C
Source: Veritas Prep
If m is the product of all integers from 1 to 40, inclusive, what is the greatest integer p for which
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If m is the product of all integers from 1 to 40, inclusive, what is the greatest integer p for which 10^p is a factor of m?(A) 7(B) 8(C) 9(D) 10(E) 11
Given: m=40! So we should find the # of trailing zeros in 40!, as it'll be the greatest value of p for which 40!/10^p will be an integer.
40! has 9 trailing zeros, which means that 40! ends with 9 zeros so p=9 is the greatest integer for which 10^p (10^9) is a factor of 40!.
Answer: C.
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Given: m=40! So we should find the # of trailing zeros in 40!, as it'll be the greatest value of p for which 40!/10^p will be an integer.
40! has 9 trailing zeros, which means that 40! ends with 9 zeros so p=9 is the greatest integer for which 10^p (10^9) is a factor of 40!.
Answer: C.
Call us at 8882156269 or live chat with us on our website if you need any GMAT Prep help! Thanks for your interest!
Manhattan Elite Prep