The GMAT Sample Math question for the day is from the topic Number Systems covering the concept of factorials in numbers and highest power of a prime number that can divide a factorial.

Question
How many zeros will be there in the value of 25!?

A. 25
B. 8
C. 6
D. 5
E. 2

The correct choice is (C) and the correct answer is 6.

Explanatory Answer
25! is factorial 25 whose value = 25*24*23*22*…..*1

When a number that has 5 as its factor is multiplied by another number that has 2 as its factor, the result will have ‘0’ in its units digit. (product of 5 and 2 is 10 and any number when multiplied with 10 or a power of 10 will have one or as many zeroes as the power of 10 with which it has been multiplied)

In 25!, the numbers that have 5 as their factor are 5, 10, 15, 20, and 25. 25 is the square of 5 and hence has two 5’s in it.

Therefore, 25! contains in it 6 fives.
There are more than 6 even numbers in 25!. Hence, the limiting factor is the number of 5s.

And hence, the number 25! will have 6 zeroes in it.

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