Long Division

What is long division?

Long division is a written method for dividing a big number by another number when the answer isn't obvious. It looks scary at first because of all the steps, but it is really just one small cycle repeated until you finish. Once you know the cycle, you can divide numbers of any size.

This lesson builds on ideas from our division made simple lesson and relies heavily on your times tables, so make sure those feel comfortable before you dive in.

The words we use

Division has three special words. Let's meet them with the example 156 ÷ 4:

• The dividend is the number being shared out — here, 156.
• The divisor is the number we share by — here, 4.
• The quotient is the answer — how much each group gets.

Anything left over that can't be shared equally is the remainder.

The magic cycle: DMSB

Every step of long division follows the same four moves, in the same order. We call it DMSB:

1. Divide — how many times does the divisor go in?
2. Multiply — multiply that answer by the divisor.
3. Subtract — take it away to see what's left.
4. Bring down — bring down the next digit and start again.

Some people remember the order with the phrase "Dad, Mum, Sister, Brother." You repeat this cycle once for each digit of the dividend.

Worked example 1: 156 ÷ 4

Set it out with the dividend under the "bus stop":

      ___
  4 ) 156

Work on the 1 (hundreds). Does 4 go into 1? No, 1 is too small. So we look at the first two digits, 15.

Cycle 1 — on the 15:

• Divide: How many 4s in 15? 4 × 3 = 12, 4 × 4 = 16 (too big). So 3. Write 3 above the 5.
• Multiply: 3 × 4 = 12.
• Subtract: 15 − 12 = 3.
• Bring down: bring down the 6 to make 36.

Cycle 2 — on the 36:

• Divide: How many 4s in 36? 4 × 9 = 36 exactly. So 9. Write 9 above the 6.
• Multiply: 9 × 4 = 36.
• Subtract: 36 − 36 = 0.
• Bring down: nothing left to bring down.

       39
  4 ) 156
     -12
      ---
       36
      -36
      ---
        0

So 156 ÷ 4 = 39 with no remainder.

Worked example 2: a remainder — 173 ÷ 5

      ___
  5 ) 173

• 5 doesn't go into 1, so start with 17.
• Divide: 5 × 3 = 15, 5 × 4 = 20 (too big). So 3.
• Multiply: 3 × 5 = 15. Subtract: 17 − 15 = 2. Bring down the 3 → 23.
• Divide: 5 × 4 = 20, 5 × 5 = 25 (too big). So 4.
• Multiply: 4 × 5 = 20. Subtract: 23 − 20 = 3. Nothing left to bring down.

The 3 can't be divided by 5, so it is the remainder.

173 ÷ 5 = 34 remainder 3 (written as 34 r3).

Worked example 3: when you need a zero — 624 ÷ 6

This one hides a trap.

• 6 into 6 = 1. Multiply 1 × 6 = 6, subtract 6 − 6 = 0. Bring down the 2 → 2.
• 6 into 2? It doesn't go! 2 is smaller than 6. So write a 0 in the answer, then bring down the 4 → 24.
• 6 into 24 = 4. Multiply 4 × 6 = 24, subtract = 0.

624 ÷ 6 = 104. That 0 in the middle is essential — without it you'd get 14, which is far too small. Whenever the divisor won't fit, you must place a 0 to keep your digits in their correct columns.

A quick reference

Step	Question you ask	What you write
Divide	How many times does it fit?	the digit, on top
Multiply	digit × divisor = ?	underneath
Subtract	take it away	the difference
Bring down	next digit comes down	new number to divide

Checking your answer

There's a lovely way to check long division using its opposite, multiplication:

quotient × divisor + remainder = dividend

For 173 ÷ 5 = 34 r3, check: 34 × 5 = 170, plus the remainder 3 = 173. It matches the original dividend, so we know we're right. If you ever feel unsure, this check will tell you.

Why long division matters

Long division teaches you to attack a big, messy problem by chopping it into tidy steps — divide, multiply, subtract, bring down, repeat. That same patient, step-by-step thinking shows up in algebra, in sharing money fairly, in working out averages, and in everyday life. It also deepens your understanding of how numbers fit together, which makes mental math sharper too.

Try it yourself

Use the DMSB cycle for each. Check every answer with multiplication.

1. 96 ÷ 4
2. 248 ÷ 8
3. 535 ÷ 5 (watch for the zero!)
4. 197 ÷ 6 (this one has a remainder)

Answers: 1) 24 2) 31 3) 107 4) 32 r5.

Once you're confident, try mixing skills with our multiplication and division word problems to see long division in real situations.