GMAT Maths Questions | Number Theory Q7

GMAT Questions | Factorials | Number of trailing zeroes

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. A GMAT 700 level sample question.

Question 7: 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

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Video Explanation

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Explanatory Answer

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

When a number that is a multiple of 5 is multiplied with 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.

Make sure you watch the explanation video embedded above for a methodical shortcut to find the number of trailing zeroes.

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