What is the greatest value of x such that 5^x is a factor...

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swerve: Legendary Member; Posts: 2539; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Wed Nov 01, 2017 9:33 am

What is the greatest value of x such that 5^x is a factor of 25! ?

A. 2
B. 3
C. 4
D. 5
E. 6

The OA is E.

I don't understand this PS question. Please, can any expert assist me with it? Thanks.

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Source: Beat The GMAT — Problem Solving | Wed Nov 01, 2017 9:33 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

re:

by DavidG@VeritasPrep » Wed Nov 01, 2017 10:50 am

swerve wrote:What is the greatest value of x such that 5^x is a factor of 25! ?

A. 2
B. 3
C. 4
D. 5
E. 6

The OA is E.

I don't understand this PS question. Please, can any expert assist me with it? Thanks.

Effectively, we want the number of 5's in the prime factorization of 25!. So, let's examine all the multiples of 5 in 25!

5 ---> one 5
10 --> one 5
15---> one 5
20 ---> one 5
25 = 5^2 ---> two 5's

Add 'em up: and we've got 6 total. The answer is E

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8142; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Nov 01, 2019 7:03 pm

swerve wrote:What is the greatest value of x such that 5^x is a factor of 25! ?

A. 2
B. 3
C. 4
D. 5
E. 6

The OA is E.

I don't understand this PS question. Please, can any expert assist me with it? Thanks.

Prime factorizing all the multiples of 5 up to 25, we have:

25 = 5^2

20 = 5^1 x 2^2

15 = 5^1 x 3

10 = 5^1 x 2

5 = 5^1

Thus, we see that there are 6 factors of 5 in 25! and thus the maximum value of x is 6.

Answer: E

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