Number Properties - Factorials, Trailing zeroes

Concept: Number of trailing zeroes, Factorials

This GMAT Math practice question is a number properties question covering the concept of factorials and the highest power of a prime number that can divide a factorial.

Question: How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?

  1. 25
  2. 8
  3. 6
  4. 5
  5. 2

Explanatory Answer

Video explanation coming soon

25! means factorial 25 whose value = 25 * 24 * 23 * 22 *....* 1

When a number that has 5 as its factor is multiplied by an even number, it results in a trailing zero.
(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 following numbers have 5 as their factor: 5, 10, 15, 20, and 25.
25 is the square of 5 and hence it has two 5s in it.
In toto, it is equivalent of having six 5s.

There are at least 6 even numbers in 25!
Hence, the number 25! will have 6 trailing zeroes in it.

Choice C is the correct answer.

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