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
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
