How many of the following numbers are divisible by 132 ? 264, 396, 462, 792,…

Answer: 4 numbers

Explanation:

132 = 2^2 × 3 × 11 = 4 × 3 × 11. Therefore a number is divisible by 132 exactly when it is divisible by 4, by 3 and by 11.

• 264: divisible by 4 (last two digits 64), by 3 (2+6+4=12), and by 11 (2-6+4=0) ⇒ divisible by 132.

• 396: divisible by 4 (96), by 3 (3+9+6=18), and by 11 (3-9+6=0) ⇒ divisible by 132.

• 462: divisible by 3 and by 11, but not by 4 (last two digits 62) ⇒ not divisible by 132.

• 792: divisible by 4 (92), by 3 (7+9+2=18), and by 11 (7-9+2=0) ⇒ divisible by 132.

• 968: divisible by 4 (68) and by 11 (9-6+8=11) but not by 3 (9+6+8=23) ⇒ not divisible by 132.

• 2178: divisible by 3 and by 11 but not by 4 (last two digits 78) ⇒ not divisible by 132.

• 5184: divisible by 4 (84) and by 3 (5+1+8+4=18) but not by 11 (5-1+8-4=8) ⇒ not divisible by 132.

• 6336: divisible by 4 (36), by 3 (6+3+3+6=18), and by 11 (6-3+3-6=0) ⇒ divisible by 132.

Therefore the numbers divisible by 132 are 264, 396, 792 and 6336. Required count = 4.