Concept 2 of 9
Long Division with Bigger Numbers
Today's big idea
A rung the divisor will not fit into still produces a digit, and that digit is 0.
When a digit you bring down is smaller than the divisor, that step still gets a 0.
How it works
👀 What's going on?
Dividing 874 by 23 took two rungs. Dividing 8,214 by 24 takes four, and somewhere in the middle the divisor will not fit at all. That empty step is where most wrong answers come from, because it is tempting to skip it.
💡 Here's the trick
Look at the worked sum above. You are sharing 8,214 into groups of 24. Three 24s fit into 82, leaving 10. Bring down the 1 to make 101, and four 24s make 96, leaving 5. Bring down the 4 to make 54, and two 24s make 48, leaving 6. So 8,214 divided by 24 is 342 with 6 left over. Every rung is one small multiplication. Sometimes the number you bring down is smaller than the divisor. The answer for that rung is 0, and that 0 must go on top before you move on.
🪄 How to do it
- 1.Take the front digits and ask how many times the divisor fits, as the sum above does with 24 into 82.
- 2.Write the digit on top, multiply, subtract, then bring the next digit down.
- 3.Write a 0 on top whenever the divisor does not fit, and carry on.
✍️ Try it
Work out 6,180 divided by 12. Watch what happens after the first rung.
12 goes into 61 five times, giving 60 and leaving 1. Bring down the 8 to make 18, and 12 fits once, leaving 6. Bring down the 0 to make 60, and 12 fits exactly 5 times. The answer is 515. Every rung produced a digit, so nothing was skipped.
⚠️ Watch out
You might be thinking a rung where the divisor does not fit can just be passed over. In 4,128 divided by 41, the second rung has 2, and 41 does not fit into 2. Skip it and you write 18 instead of 100 remainder 28. The 0 is holding a place, exactly as it does in a written number.
🌟 Why this matters
Splitting a monthly total across a year, or a delivery into crates, runs to numbers this size. Writing each rung down means a slip shows up in one line instead of poisoning the whole answer.
Exam tip: Count the digits of your answer against the rungs you worked, and a skipped 0 shows up at once.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Work out 4,128 ÷ 41.”
- 1
First rung
41 into 41 goes 1. Subtract 41, nothing left.
- 2
Bring down the 2
Now you have just 2, and 41 does not fit into 2.
- 3
Write the 0 — do not skip
Put 0 on top and bring the next digit down. Skipping it turns 100 into 18.
- 4
Last rung ✓
28 is left, so 4,128 ÷ 41 = 100 r 28
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
THE PROBLEM
4,128 ÷ 41
?answer so far
41 ) 4128
this rung has 41 to share
How many 41s fit into 41?
Quick check
✅ VERIFICATION
Dividing 4,128 by 41, what happens at the rung where you have only 2 to share?
⚡ Finish the activity above first to answer.
Keep going!
Up next: What to Do With the Remainder
Remainder, fraction or decimal, chosen by what you are sharing.