How to Do Long Division (Without Losing Your Mind)

It looks scary. It's actually just four little steps on a loop. Let's tame it together.

· 9 min read

Be honest: when you see a long division problem, does a little part of your brain quietly whisper "nope"? You are very much not alone. Long division is the math topic that makes the most grown adults break into a cold sweat.

Here's the secret nobody tells you: long division isn't one big hard thing. It's four tiny easy things that you just keep repeating. Once you see the pattern, you can't un-see it. Let's go.

First, meet the cast of characters

Every long division problem has three main parts. Get friendly with these names and the rest is easy:

1564624Quotient(your answer)Divisor(what you divide by)Dividend(the number being split up)

The big number going in, the small number doing the splitting, and the answer sitting on the roof.

The whole trick: four steps, on repeat

Long division is just this little loop, over and over, until you run out of digits. To remember the order, say:

"Does McDonald's Serve Burgers?"

Step 1 · D
Divide

How many times does the divisor fit into the digit(s) you're looking at? Write that number up top.

Step 2 · M
Multiply

Multiply that top number by the divisor. Write the answer underneath.

Step 3 · S
Subtract

Subtract to see what's left over. (It should always be smaller than the divisor.)

Step 4 · B
Bring down

Bring down the next digit and stick it beside the leftover. Then go back to Step 1.

That's it. That's the whole thing. When there are no more digits to bring down, you're done, and whatever is left at the bottom is your remainder.

Worked example #1: 624 ÷ 4

Let's run the loop. We're sharing 624 into 4 equal groups.

  • Divide: 4 goes into 6 once. Write 1 on top.
  • Multiply: 1 × 4 = 4. Write 4 under the 6.
  • Subtract: 6 − 4 = 2.
  • Bring down: bring down the 2 to make 22. Now repeat: 4 into 22 goes 5 times (5 × 4 = 20, leftover 2). Bring down the 4 to make 24. 4 into 24 goes 6 times exactly.
    1 5 6
  ─────────
4 │ 6 2 4
    4
    ─
    2 2
    2 0
    ─
      2 4
      2 4
      ─
        0
Answer: 624 ÷ 4 = 156. Check it by multiplying back: 156 × 4 = 624. It matches, so you nailed it.

Worked example #2: 754 ÷ 3 (this one has a remainder)

Same loop, but this time it won't divide perfectly, and that's totally fine.

  • Divide: 3 goes into 7 twice. Write 2 on top.
  • Multiply and subtract: 2 × 3 = 6, and 7 − 6 = 1.
  • Bring down the 5 to make 15. 3 into 15 goes 5 times exactly. Bring down the 4 to make 4.
  • 3 goes into 4 once (1 × 3 = 3), leaving 1. There are no more digits to bring down, so 1 is the remainder.
    2 5 1
  ─────────
3 │ 7 5 4
    6
    ─
    1 5
    1 5
    ─
        4
        3
        ─
        1
Answer: 754 ÷ 3 = 251 remainder 1 (you might also write it as "251 R1"). Check it: 251 × 3 = 753, plus the remainder 1 = 754.

Pro tips that make it way easier

  • Keep your columns neat. Most long division mistakes aren't math mistakes, they're lining-up mistakes. Grid paper is your best friend.
  • Don't panic when it doesn't fit. If the divisor doesn't go into a digit (say, 4 into 3), write a 0 up top and bring down the next digit.
  • Always check by multiplying back. Quotient × divisor (+ remainder) should equal the dividend. Free peace of mind.
  • Know your times tables. Long division leans hard on multiplication. A quick times-table refresher pays off more than anything else.

Your turn: practice problems

Grab a pen. Run the loop. No peeking until you've tried.

  1. 372 ÷ 4
  2. 845 ÷ 5
  3. 588 ÷ 6
  4. 947 ÷ 4 (this one has a remainder)
Tap to reveal the answers
  • 1. 372 ÷ 4 = 93
  • 2. 845 ÷ 5 = 169
  • 3. 588 ÷ 6 = 98
  • 4. 947 ÷ 4 = 236 remainder 3

Why this matters for the CAEC

The CAEC math test rewards solid, confident arithmetic, and long division shows up in everyday problems like splitting costs, figuring out unit prices, and working with fractions. The more automatic it feels, the more brainpower you free up for the tricky word problems.

Want more practice like this? Our CAEC math guide and the CAEC Ready Workbook are packed with worked examples and practice questions, or start with a free math sample to test yourself.

Disclaimer

This article is a general math tutorial for study purposes. CAEC Ready is an independent study resource and is not affiliated with or endorsed by any government, ministry of education, or official CAEC testing provider.

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