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For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. In how many ways can 9! be
expressed as a product of 2 positive integers?
expressed as a product of 2 positive integers?
- a)36
- b)72
- c)79
- d)80
- e)160
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
For any integer P greater than 1, P! denotes the product of all the in...
Given:
P > 1
P! = 1 x 2 x 3…x P
P! = 1 x 2 x 3…x P
To Find
# of ways
in which 9! can be written
as a x b , where a, b are integers > 0
# of ways
in which 9! can be written
as a x b , where a, b are integers > 0
Approach:
1. Note the nature of numbers a,b in the product . a x b.
a,b are both factors of 9!.
a,b are both factors of 9!.
Let’s take a simple example to understand the above application. Let’s take the number 6.
Its factors are – 1, 2, 3, 6 - i.e. 4 factors
It can be expressed as product of two numbers as follows
1 x 6
2 x 3
Its factors are – 1, 2, 3, 6 - i.e. 4 factors
It can be expressed as product of two numbers as follows
1 x 6
2 x 3
Working out:
9! can be expressed as a product of two positive numbers in 80 ways. Choice D is the correct answer.
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For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. In how many ways can 9! beexpressed as a product of 2 positive integers?a)36b)72c)79d)80e)160Correct answer is option 'D'. Can you explain this answer?
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For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. In how many ways can 9! beexpressed as a product of 2 positive integers?a)36b)72c)79d)80e)160Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. In how many ways can 9! beexpressed as a product of 2 positive integers?a)36b)72c)79d)80e)160Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. In how many ways can 9! beexpressed as a product of 2 positive integers?a)36b)72c)79d)80e)160Correct answer is option 'D'. Can you explain this answer?.
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