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 related to GMAT. Concepts covered in this eBook include LCM, HCF, remainder theorem, units digits, remainders and factorials in number theory.
The book contains 33 solved examples and about 20 illustrative examples. In addition, the eBook contains 25 exercise questions covering a wide variety of questions from the topic.
This eBook has 80 Problem Solving questions and 49 Data Sufficiency questions in Number Properties and Number Theory. Concepts covered include LCM, HCF, remainder theorem in number theory, factors, factorials and numerous word problems. Detailed explanatory answers provided to each question.
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Topicwise List of Questions
This eBook covers all the topics in Number Theory related to GMAT. Concepts covered in this eBook include LCM, HCF, remainder theorem, units digits, remainders and factorials in number theory. 
This eBook has 80 Problem Solving questions and 49 Data Sufficiency questions in Number Properties and Number Theory. Concepts covered include LCM, HCF, remainder theorem in number theory, factors, factorials and numerous word problems. Detailed explanatory answers provided to each question.
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