7^m is a factor of n/7^2?

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Mar 12, 2012 2:33 am

If n is the product of the integers from 1 to 70, inclusive, what is the greatest integer m for which 7^m is a factor of n/7^2?
(A) 2
(B) 7
(C) 9
(D) 11
(E) 14

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Source: Beat The GMAT — Problem Solving | Mon Mar 12, 2012 2:33 am

killer1387: Legendary Member; Posts: 581; Joined: Sun Apr 03, 2011 7:53 amFollowed by: 5 members; Thanked: 52 times

by killer1387 » Mon Mar 12, 2012 2:55 am

sanju09 wrote:If n is the product of the integers from 1 to 70, inclusive, what is the greatest integer m for which 7^m is a factor of n/7^2?
(A) 2
(B) 7
(C) 9
(D) 11
(E) 14

Total number of 7 in 70!=11
hence n/7^2 has 11-2 =9 7's

option C.

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