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

The numbers divisible by 132 are: 264, 396, 792, and 6336, so the answer is 4. Quick way to see it:

• 132=22×3×11132=2^2\times 3\times 11132=22×3×11, so a number is divisible by 132 if it is divisible by 4, 3, and 11.
• Check each:
  1. • Divisible by 4: last two digits 64 ÷ 4 = 16
     • Divisible by 3: 2 + 6 + 4 = 12, which is divisible by 3
     • Divisible by 11: (2 + 4) − 6 = 0, which is divisible by 11
       ⇒ divisible by 132 ✅
  2. • Last two digits 96 ÷ 4 = 24 ⇒ divisible by 4
     • 3 + 9 + 6 = 18 ⇒ divisible by 3
     • (3 + 6) − 9 = 0 ⇒ divisible by 11
       ⇒ divisible by 132 ✅
  3. • Last two digits 62 is not divisible by 4
       ⇒ not divisible by 132 ❌
  4. • Last two digits 92 ÷ 4 = 23 ⇒ divisible by 4
     • 7 + 9 + 2 = 18 ⇒ divisible by 3
     • (7 + 2) − 9 = 0 ⇒ divisible by 11
       ⇒ divisible by 132 ✅
  5. • Last two digits 68 ÷ 4 = 17 ⇒ divisible by 4
     • 9 + 6 + 8 = 23 ⇒ not divisible by 3
       ⇒ not divisible by 132 ❌
  6. • Last two digits 78 is not divisible by 4
       ⇒ not divisible by 132 ❌
  7. • Last two digits 84 ÷ 4 = 21 ⇒ divisible by 4
     • 5 + 1 + 8 + 4 = 18 ⇒ divisible by 3
     • (5 + 8) − (1 + 4) = 13 − 5 = 8 ⇒ not divisible by 11
       ⇒ not divisible by 132 ❌
  8. • Last two digits 36 ÷ 4 = 9 ⇒ divisible by 4
     • 6 + 3 + 3 + 6 = 18 ⇒ divisible by 3
     • (6 + 3) − (3 + 6) = 9 − 9 = 0 ⇒ divisible by 11
       ⇒ divisible by 132 ✅

So, 4 of the given numbers are divisible by 132.