Pengi Editor's Note: This article was originally published by Think Academy. We're sharing it here for educational value. Think Academy is a leading K-12 math education provider.
How to Divide 3-Digit by 2-Digit Numbers in 3 Easy Steps
Dividing 3-digit numbers by 2-digit numbers uses the same long division process as simpler division, but requires more careful estimation at each step. This guide breaks it down with clear examples.
Review: The Division Process (D-M-S)
Long division always follows:
- Divide: How many times does the divisor go into the current dividend chunk?
- Multiply: Multiply the quotient digit by the divisor.
- Subtract: Subtract the product from the dividend chunk, then bring down the next digit.
Example 1: 672 ÷ 21
Step 1: Look at the first two digits: 67.
How many times does 21 go into 67?
Estimate: 21 × 3 = 63, 21 × 4 = 84 (too big)
21 goes into 67 three times (3)
Write 3 above the 7 in 672.
Step 2: Multiply
3 × 21 = 63
Step 3: Subtract
67 − 63 = 4
Bring down the next digit (2) → now have 42.
Repeat:
How many times does 21 go into 42?
21 × 2 = 42 → exactly 2 times
Write 2 above the 2 in 672.
2 × 21 = 42
42 − 42 = 0
Answer: 672 ÷ 21 = 32
Check: 32 × 21 = 672 ✓
Example 2: 945 ÷ 35
Step 1: Look at 94.
35 × 2 = 70, 35 × 3 = 105 (too big)
35 goes into 94 twice (2)
Write 2 above the 4.
Step 2: Multiply
2 × 35 = 70
Step 3: Subtract
94 − 70 = 24
Bring down 5 → 245.
Repeat:
35 × 7 = 245 → exactly 7 times
Write 7 above the 5.
7 × 35 = 245
245 − 245 = 0
Answer: 945 ÷ 35 = 27
Example 3: Division with Remainder — 587 ÷ 24
Step 1: Look at 58.
24 × 2 = 48, 24 × 3 = 72 (too big)
24 goes into 58 twice (2)
Step 2: Multiply
2 × 24 = 48
Step 3: Subtract
58 − 48 = 10
Bring down 7 → 107.
Repeat:
24 × 4 = 96, 24 × 5 = 120 (too big)
24 goes into 107 four times (4)
4 × 24 = 96
107 − 96 = 11
Answer: 587 ÷ 24 = 24 remainder 11 (or 24 R11)
Check: 24 × 24 = 576; 576 + 11 = 587 ✓
Estimation Strategy for Step 1
When the divisor is a 2-digit number, estimation helps you find the quotient digit quickly:
- Round the divisor to the nearest 10.
- Use that rounded number to estimate.
Example: 348 ÷ 16
Round 16 to 20. How many times does 20 go into 34? → about 1 time.
Verify: 1 × 16 = 16 (OK, try 2: 2 × 16 = 32, which is ≤ 34 ✓)
3 × 16 = 48 (too big)
So the quotient digit is 2.
Common Challenges
Underestimating the quotient digit: If your estimate is too small, you'll find that after subtracting, the remainder is ≥ the divisor. If this happens, go back and increase the quotient digit by 1.
Overestimating the quotient digit: If your product is bigger than the dividend chunk, decrease the quotient digit by 1.
Practice Problems
- 528 ÷ 24 = ?
- 756 ÷ 36 = ?
- 897 ÷ 42 = ?
- 432 ÷ 16 = ?
- 605 ÷ 25 = ?
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