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

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

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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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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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