## Question

**How many of the following numbers are divisible by 132?**

264, 396, 462, 792, 968, 2178, 5184, 6336

264, 396, 462, 792, 968, 2178, 5184, 6336

A. 3

B. 4

C. 6

D. 8

#### Answer: B

**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:**

**What is the largest 4 digit number exactly divisible by 88?**