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Byju's Answer
Standard XII
Mathematics
Factorial
Let N = 22×...
Question
Let N =
2
2
×
3
3
×
7
4
How many factors of
N
2
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
=
2
2
×
3
3
×
7
4
The number of factors of
N
are
3
×
4
×
5
=
60
N
2
=
2
4
×
3
6
×
7
8
The number of factors of
N
2
are
5
×
7
×
9
=
315
Among
315
−
1
=
314
factors , half are less than
N
, which implies
157
factors of
N
2
are less than
N
Number of Factors of
N
which are less than
N
are
60
−
1
=
59
Therefore number of factors of
N
2
which are less than
N
and not the factors of
N
are
157
−
59
=
98
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