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

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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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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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