Divisibility Tests

Class 6 Maths · Chapter 5: Prime Time · NCERT Ganita Prakash section 5.5

Learn

Can we tell if a big number divides by 10, 5 or 2 without dividing? Yes, just look at the last digit. Divisible by 10: ends in 0. By 5: ends in 0 or 5. By 2: ends in 0, 2, 4, 6 or 8.

Why does this work? Any number is some tens plus its last digit, and every ten divides by 10, 5 and 2. So only the last digit decides!

4,736 = 473 × 10 + 6

Divisible by 4: 100 divides by 4, so only the last two digits matter. 5,316 → 16 ÷ 4 = 4, so 5,316 divides by 4. Divisible by 8: 1,000 divides by 8, so look at the last three digits. 27,104 → 104 ÷ 8 = 13 ✓.

5,316 → 16 ÷ 4 = 4 · 27,104 → 104 ÷ 8 = 13

Explore: turn the digit wheels to build numbers that pass the tests.

1. Make a 3-digit number that divides by 5 but not by 10.
2. Make a 3-digit number that divides by 4 but not by 8.
3. Make a 3-digit number that divides by 8.

Remember

• 10: last digit 0. 5: last digit 0 or 5. 2: last digit even.
• 4: the last two digits divide by 4. 8: the last three digits divide by 8.

Quick check

Which number is divisible by 4?

1. 3,418
2. 7,236
3. 5,142
4. 9,330

Think about it

If a number divides by 8, must it divide by 4? If it divides by 4, must it divide by 8?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.