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

Given data

• Test divisibility by 132 for: 264, 396, 462, 792, 968, 2178, 5184, 6336.

Concept / Approach

• Prime factorize 132: 132 = 2² × 3 × 11.
• Hence, a number must be divisible by 4, by 3, and by 11 to be divisible by 132.
• Quick checks: /4 ⇒ last two digits multiple of 4; /3 ⇒ sum of digits multiple of 3; /11 ⇒ alternating sum rule.

Step-by-step checks

• 264: 132 × 2 ⇒ divisible ✓
• 396: 132 × 3 ⇒ divisible ✓
• 462: /4? last two digits 62 (not /4) ⇒ not divisible ✗
• 792: 132 × 6 ⇒ divisible ✓
• 968: /4 yes (68/4), /3? 9+6+8=23 (no) ⇒ not divisible ✗
• 2178: /3 yes (2+1+7+8=18), /4? 78/4 not integer ⇒ not divisible ✗
• 5184: /4 yes (84/4), /3 yes (5+1+8+4=18), /11? (5+8) − (1+4) = 8 ≠ 0, ±11 ⇒ not divisible ✗
• 6336: 132 × 48 ⇒ divisible ✓

Count

Divisible: 264, 396, 792, 6336 ⇒ total = 4

Common pitfalls

• Checking only /4 and /3 but forgetting the /11 rule for divisibility by 132.

Final Answer

4