Divisibility by 4, 6 and 8
Level 2 Divisibility rules · Reviewed by The NumThink editorial team · Last reviewed
This page is part of the NumThink Divisibility rules course. Read why the method works, watch it run on worked examples, then drill it in the practice box below until it feels automatic.
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100 divides by 4, so every hundred and thousand is a multiple of 4, and only the last two digits can leave a remainder: 7,316 = 7,300 + 16.
1,000 divides by 8 (8 × 125 = 1,000), so for 8 the last three digits decide. And 6 = 2 × 3, so a number divides by 6 exactly when it divides by both 2 and 3.
The steps
- ÷4: take the last two digits. 7,316 → 16. 16 ÷ 4 = 4 with nothing left, so 7,316 divides by 4.
- ÷8: take the last three digits. 5,320 → 320. 320 ÷ 8 = 40, so 5,320 divides by 8.
- ÷6: test 2 and 3. 522 is even, and 5 + 2 + 2 = 9 divides by 3, so 522 divides by 6.
Worked examples
Easy Remainder of 7316 ÷ 4
Show the thinking
Last two digits: 16
16 ÷ 4 = 4, nothing left
So 7,316 ÷ 4 leaves 0.
Answer: 0
Medium Remainder of 4382 ÷ 4
Show the thinking
Last two digits: 82
82 = 80 + 2, and 80 ÷ 4 = 20
So 4,382 ÷ 4 leaves 2.
Answer: 2
Hard Remainder of 25390 ÷ 4
Show the thinking
Last two digits: 90
90 = 88 + 2, and 88 ÷ 4 = 22
So 25,390 ÷ 4 leaves 2.
Answer: 2
When to use it
- Leap years: a year divisible by 4 is a leap year (except most century years) — 2028 is one, because 28 ÷ 4 = 7.
- Packing: 1,344 items fill boxes of 8 exactly, because 344 ÷ 8 = 43.
When NOT to use it
- For the remainder of ÷6 there is no digit shortcut — the 2-and-3 test answers yes or no; divide if you need the remainder.
- Numbers under 100 — the times tables are quicker.