CLASS 8 MATHS · PLAYING WITH NUMBERS

Divisibility rules and missing digits

By 3 or 9: digit sum divisible by 3 or 9. By 11: difference of alternate digit sums is 0 or a multiple of 11.

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Worked examples

Example 1 · level 1

Which of these numbers is divisible by 4?

1915
6016
7931
1323

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Rule for 4: last two digits form a multiple of 4.
6016 passes the test: 6016 = 4 × 1504.

Answer: 6016

Example 2 · level 2

Find the smallest digit A that makes 989A divisible by 3.

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Known digit sum = 26.
26 + 1 = 27, a multiple of 3.
So A = 1.

Answer: 1

Example 3 · level 3

Find the digit A that makes 8984A divisible by 11.

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Odd places (from right): 8 + 8 + A; even places: 9 + 4.
With A = 8: 89848 gives a difference of 11, which is 0 or a multiple of 11.
So A = 8.

Answer: 8