The GMAT Sample Math question 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 7
How many trailing zeros will be there after the rightmost non-zero digit 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 5s 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 trailing zeroes in it.
This eBook covers all the topics in Number Theory and Inequalities related to GMAT. Explanation of topics provide in-depth knowledge of concepts such as LCM, HCF, remainder theorem in number theory and the rules governing inequalities.
The book contains over 50 solved examples and illustrative examples. In addition, the eBook contains 44 exercise questions covering a wide variety of questions from these two topics for you to practise.
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Topicwise List of Questions
This eBook covers all the topics in Number Theory and Inequalities related to GMAT. Explanation of topics provide in-depth knowledge of concepts such as LCM, HCF, remainder theorem in number theory and the rules governing inequalities. 
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