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Apply the divisibility rule for 11 to 8,591: the digits in the odd places add to 1 + 5 = 6 and the digits in the even places add to 9 + 8 = 17. Is 8,591 divisible by 11?

Class 6Playing with NumbersPlaying with Numbers
  • ANo — the difference is 11, and it has to be exactly 0.
  • BNo — 8,591 is odd, so 11 cannot divide it.
  • CYes — the difference is 17 − 6 = 11, which is a multiple of 11.
  • DYes — the digit sum 8 + 5 + 9 + 1 = 23 is not a multiple of 2.

Step-by-Step Solution

The rule accepts a difference of 0 or of any multiple of 11, and here the difference is 11 — so 8,591 is divisible by 11. Checking, . The traps are demanding a difference of exactly 0, and reaching for the digit-sum test, which belongs to 3 and 9 rather than to 11.
Answer: C) Yes — the difference is 17 − 6 = 11, which is a multiple of 11.

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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