Question:
If \(N = 2^5 \times 3^4 \times 5^5 \times 11^2\), then how many factors of N are multiples of 66 but not of 72?
If \(N = 2^5 \times 3^4 \times 5^5 \times 11^2\), then how many factors of N are multiples of 66 but not of 72?
Updated On: Sep 13, 2024
- 136
- 130
- 132
- 122
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The Correct Option is C
Solution and Explanation
The correct option is (C): 132.
66 = 2 x 3 x 11
LCM of 66 and 72 = 792 = 23 x 32 x 11
N = 25 x 34 x 55 x 112 = (2 x 3 x 11) x 24 x 33 x 55 x 11
So, the number of multiples of 66 = (4 + 1) x (3 + 1) x (5 + 1) x (1 + 1)= 240
N = 25 x 34 x 55 x 112 = (23 x 32 x 11) x 22 x 32 x 55 x 11
So, the number of multiples of 792 = (2 + 1) x (2 + 1) x (5 + 1) x (1 +1) = 108
Answer = Number of multiples of 66 – Number of multiples of 792 = 240– 108 = 132.
66 = 2 x 3 x 11
LCM of 66 and 72 = 792 = 23 x 32 x 11
N = 25 x 34 x 55 x 112 = (2 x 3 x 11) x 24 x 33 x 55 x 11
So, the number of multiples of 66 = (4 + 1) x (3 + 1) x (5 + 1) x (1 + 1)= 240
N = 25 x 34 x 55 x 112 = (23 x 32 x 11) x 22 x 32 x 55 x 11
So, the number of multiples of 792 = (2 + 1) x (2 + 1) x (5 + 1) x (1 +1) = 108
Answer = Number of multiples of 66 – Number of multiples of 792 = 240– 108 = 132.
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