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Divisibility by 2, 5 and 10: Look at the Last Digit

Level 1 Divisibility rules · Reviewed by The NumThink editorial team · Last reviewed

Short version: Only the last digit matters: even → divisible by 2; 0 or 5 → by 5; 0 → by 10. The remainder comes from the last digit too: 953 ÷ 10 leaves 3.

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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Why it works

Every number is a multiple of 10 plus its last digit: 953 = 950 + 3. Tens, hundreds and thousands all divide exactly by 2, 5 and 10, so only the last digit can leave anything over.

So the whole number leaves the same remainder as its last digit: 953 ÷ 5 leaves the same as 3 ÷ 5, which is 3.

The steps

  1. Look only at the last digit. In 4,376 it is 6.
  2. Apply the rule. Even → divisible by 2. Ends in 0 or 5 → by 5. Ends in 0 → by 10.
  3. For the remainder, divide just the last digit. 4,376 ÷ 5: 6 ÷ 5 leaves 1.

Worked examples

Easy Remainder of 691 ÷ 2

Show the thinking

The last digit is 1 — odd

1 ÷ 2 leaves 1

So 691 ÷ 2 leaves 1.

Answer: 1

Medium Remainder of 953 ÷ 5

Show the thinking

The last digit is 3

3 ÷ 5 leaves 3

So 953 ÷ 5 leaves 3.

Answer: 3

Hard Remainder of 4378 ÷ 5

Show the thinking

The last digit is 8

8 ÷ 5 leaves 3

So 4,378 ÷ 5 leaves 3.

Answer: 3

When to use it

  • Sharing equally: 138 candies split evenly between 2 children (it is even), but not between 5 (it ends in 8).
  • Checking answers: any multiple of 10 must end in 0.

When NOT to use it

  • Other divisors: the last digit says nothing about 3 or 9 — 13 and 33 both end in 3, but only 33 divides by 3.
  • 4 and 8 need the last two or three digits — see the 4, 6 and 8 lesson.

Common mistakes

Using the digit sum for 2 or 5. Adding the digits of 346 to test it for 5. Fix: For 2, 5 and 10 only the last digit counts: 346 ends in 6, so it does not divide by 5.
Thinking "ends in 5" works for 10. Saying 85 divides by 10. Fix: Only a last digit of 0 works for 10: 85 ÷ 10 leaves 5.
Check yourself: Check with a nearby multiple: 950 divides by 5 and 953 is 3 more, so the remainder is 3 ✓.