Question:
How many odd factors of the number 456 x 565 x 776 are multiples of 63?
How many odd factors of the number 456 x 565 x 776 are multiples of 63?
Updated On: Nov 17, 2025
- 5823
- 5929
- 4943
- 5943
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The Correct Option is B
Solution and Explanation
The correct option is (B): 5929.
456 x 565 x 776 = (32 x 5)6 x (23 x 7)5 x (7 x 11)6
= 215 x 312 x 56 x 711 x 116
63 = 32 x 7
So, after removing 212 and (32 x 7) from the given number,
The remaining number = 310 x 56 x 710 x 116
So, the required number of factors = (10 + 1) (6 + 1) (10 + 1) (6 + 1) =5929
456 x 565 x 776 = (32 x 5)6 x (23 x 7)5 x (7 x 11)6
= 215 x 312 x 56 x 711 x 116
63 = 32 x 7
So, after removing 212 and (32 x 7) from the given number,
The remaining number = 310 x 56 x 710 x 116
So, the required number of factors = (10 + 1) (6 + 1) (10 + 1) (6 + 1) =5929
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