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Question

Let N = 22×33×74
How many factors of N2 which are less than N are not the factors of N?

A
91
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B
92
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C
98
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D
94
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Solution

The correct option is C 98
Given N=22×33×74
The number of factors of N are 3×4×5=60
N2=24×36×78
The number of factors of N2 are 5×7×9=315
Among 3151=314 factors , half are less than N , which implies 157 factors of N2 are less than N
Number of Factors of N which are less than N are 601=59
Therefore number of factors of N2 which are less than N and not the factors of N are 15759=98


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