 # How many of the following numbers are divisible by 132?264, 396, 462, 792, 968, 2178, 5184, 6336

## Question

### How many of the following numbers are divisible by 132?264, 396, 462, 792, 968, 2178, 5184, 6336

`A. 3`
`B. 4`
`C. 6`
`D. 8`

Solution:

132 = 3 × 4 × 11 where 3, 4 and 11 are pairwise co-prime numbers. Also, 3,4 and 11 are factors of 132. Hence,
(1) if a number is divisible by 3, 4 and 11, the number will be divisible by their product 132 also.
(2) If a number is not divisible by 3 or 4 or 11, it is not divisible by 132

264 is divisible by 3, 4 and 11
=> 264 is divisible by 132

396 is divisible by 3, 4 and 11
=> 396 is divisible by 132

462 is divisible by 3 and 11, but not divisible by 4
=> 462 is not divisible by 132

792 is divisible by 3, 4 and 11
=> 792 is divisible by 132

968 is divisible by 4 and 11, but not divisible by 3
=> 968 is not divisible by 132

2178 is divisible by 3 and 11, but not divisible by 4
=> 2178 is not divisible by 132

5184 is divisible by 3 and 4, but not divisible by 11
=> 5184 is not divisible by 132

6336 is divisible by 3, 4 and 11
=> 6336 is divisible by 132

Hence, only 264, 396 ,792 and 6336 are divisible by 132. So the answer is 4

### Related To:

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