How do you do short division?

Work through the dividend one digit at a time, left to right. Divide the first digit, write the whole part of the answer above, and carry anything left over onto the front of the next digit. For 852 / 4: 8 / 4 = 2; 5 / 4 = 1 carry 1; the carry makes the last digit 12, and 12 / 4 = 3. Answer 213.

How does long division work?

Four moves, repeated: divide, multiply, subtract, bring down. Divide to see how many times the divisor fits, multiply to see how much that used, subtract to find what is left, bring down the next digit and repeat. It is short division with the leftovers written out instead of carried in your head - which is why it works for two-digit divisors where your head runs out of room.

The part too small to share out again. 17 / 5 is 3 remainder 2: five threes use 15, and the 2 left over is less than one more share of 5. The remainder is always smaller than the divisor - if it were not, another share would fit.

How do you divide by 4 or 8 in your head?

Halve repeatedly. Dividing by 4 is halving twice; dividing by 8 is halving three times. 156 / 4: half is 78, half again is 39. This works because 4 is 2 x 2, so dividing by 4 is dividing by 2, twice.

How can you tell if a number divides exactly?

Divisibility tests: a number divides by 2 if it ends in an even digit, by 5 if it ends in 0 or 5, by 3 if its digit sum divides by 3, and by 9 if its digit sum divides by 9. 738: digit sum 18, so it divides by both 3 and 9 - no division needed to know it.

Division

Division has a reputation, and it is unearned. Every division question is a multiplication question read backwards: 72 ÷ 8 is just "8 times what makes 72?" If you know your times tables, you already hold the answers — this guide is about reading them out, from quick head methods to full long division, one step at a time.

What division means (two pictures)

Sharing: 12 sweets between 3 friends — how many each? Grouping: 12 sweets, bags of 3 — how many bags? Both are 12 ÷ 3 = 4, and both pictures matter: sharing is how children meet division, grouping is the one that scales up (long division is grouping, done systematically).

The two pictures are why 12 ÷ 3 answers two different real questions with one number. Mathematics is not being vague here — it is being efficient.

Dividing in your head

Step 1: read the times table backwards

56 ÷ 7 → "seven times what is 56?" → 8. No new skill; a fact you own, read in the other direction.

Step 2: divide by 4 and 8 by halving

÷ 4 = halve, then halve again. 156 ÷ 4 → 78 → 39.
÷ 8 = halve three times. 328 ÷ 8 → 164 → 82 → 41.

4 is 2 × 2 and 8 is 2 × 2 × 2, so dividing by them is dividing by 2 the right number of times. Halving is the one division everyone is fast at — this trick spends it three times instead of asking for anything new.

Step 3: divide by splitting

Peel off an easy multiple of the divisor, share the rest.

91 ÷ 7 → peel off 70 (ten 7s) → 21 left (three 7s) → 10 + 3 = 13.

This works because division distributes over the split: (70 + 21) ÷ 7 = 70 ÷ 7 + 21 ÷ 7. You chose the split so both parts are easy — that choice is the whole skill.

Short division, digit by digit

When the number is too big for head-methods, work left to right, one digit at a time, carrying the leftover.

852 ÷ 4:

8 ÷ 4 = 2, nothing left over.
5 ÷ 4 = 1, remainder 1 — the 1 carries onto the front of the next digit.
That makes the last digit 12. 12 ÷ 4 = 3.

Answer: 213. Check: 213 × 4 = 852. ✓

The carry is place value doing its job. The "1" left over from the tens column is one ten — put next to the 2 ones it makes twelve ones. Short division is just sharing each column and passing the change down.

Long division, without fear

Long division is short division with the leftovers written out instead of carried in your head — which is exactly why it works when the divisor has two digits and your head runs out of room. Four moves, repeated until done:

Divide — how many times does the divisor fit? Write it on top.
Multiply — how much did that use up?
Subtract — what is left?
Bring down the next digit, and repeat.

936 ÷ 24:

24 into 93 fits 3 times (3 × 24 = 72). Write 3.
93 − 72 = 21 left.
Bring down the 6 → 216.
24 into 216 fits 9 times exactly (9 × 24 = 216). Write 9. Nothing left.

Answer: 39. Check: 39 × 24 = 936. ✓

Divide–multiply–subtract–bring down is not a magic chant. Each pass answers "how many whole groups fit, and what is still unshared?" — grouping, made systematic. The subtraction line IS the remainder so far; bringing down a digit is moving to the next place value with that remainder in hand.

Remainders: the bit too small to share

17 ÷ 5 = 3 remainder 2 — five threes use 15, and the 2 left is less than one more share.

A remainder is always smaller than the divisor — if it were not, another share would fit. That one sentence is also the test for whether you have finished a long division pass.

What you do with a remainder depends on the question: 17 people in cars of 5 need 4 cars (round up); £17 shared by 5 is £3.40 each (keep dividing into decimals).

Telling it divides — without dividing

Divides by	Test	Example
2	ends in an even digit	374 ✓
5	ends in 0 or 5	485 ✓
3	digit sum divides by 3	738 → 18 ✓
9	digit sum divides by 9	738 → 18 ✓
10	ends in 0	730 ✓

The digit-sum tests work because 10, 100, 1000… each leave remainder 1 when divided by 9 (and by 3). So every digit contributes just itself to the remainder — the sum of digits carries the same remainder as the whole number. It feels like a party trick; it is place value again.

Learn it properly in the app

Each move above is a full lesson in Math Challenge, with pictures and try-it problems:

Sharing Equally — what division is.
Halving to Divide — ÷4 is halve and halve again.
Dividing by Splitting — peel off ten of the divisor, share the rest.
Long Division — divide, multiply, subtract, bring down, repeat.
Remainders — the bit too small to share out again.
Dividing Exactly and Divisibility Tests — in the Divisibility Rules ladder.

Find them in the Basic Arithmetic lessons and the Divisibility Rules lessons — all of the ones above are free.

Practice it in the game

The Division topic serves division with whole-number answers, growing from table facts up to hard-mode questions like 3648 ÷ 48 — dividends up to four digits with two-digit divisors — so every question is checkable by multiplying back.

Your turn

Three to try — tap what you get.

91 ÷ 7

156 ÷ 12

What is the remainder of 50 ÷ 7?

Practice division free →