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Sunita wants to know whether 3,512 is divisible by 8 without doing the long division. Which check does the divisibility rule for 8 ask her to make?

Class 6Playing with NumbersPlaying with Numbers
  • AWhether the last digit, 2, is divisible by 8.
  • BWhether the last two digits, 12, are divisible by 8.
  • CWhether the digit sum 3 + 5 + 1 + 2 = 11 is divisible by 8.
  • DWhether the last three digits, 512, are divisible by 8.

Step-by-Step Solution

For 8 you test the last THREE digits: 512 ÷ 8 = 64, so 3,512 is divisible by 8. The trap is borrowing a rule that belongs to a different divisor — the last-two-digits test is for 4, the last-digit test is for 2, and the digit-sum test is for 3 and 9.
Answer: D) Whether the last three digits, 512, are divisible by 8.

Key idea: Quick divisibility tests

Some checks are so fast you can do them in your head:

- **By 2**: the last digit is even (0, 2, 4, 6, or 8).
- **By 3**: the sum of the digits is divisible by 3. (273 → 2 + 7 + 3 = 12 → 12 ÷ 3 = 4 ✓)
- **By 5**: the last digit is 0 or 5.
- **By 9**: the sum of the digits is divisible by 9.
- **By 10**: the last digit is 0.
- **By 4**: the last two digits form a number divisible by 4.

These let you spot factors without doing the full division.

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