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Divide Multi-Digit
Numbers

Master the standard long division algorithm to fluently divide numbers with multiple digits: step by step, no shortcuts skipped.

6th Grade Math

What Is Division?

Division is the operation that answers: "How many equal groups can I make?" When we write \( 846 \div 3 \), we are asking how many times \( 3 \) fits into \( 846 \).

Dividend
The number being divided: \( 846 \)
Divisor
The number you divide by: \( 3 \)
Quotient
The answer (result): \( 282 \)

Why Long Division Matters

Many real-world problems require dividing large numbers: splitting costs, converting units, finding averages. The standard algorithm gives you a reliable, step-by-step method that works for any size numbers.

Splitting Costs
\( \$1{,}248 \div 4 \) friends = \( \$312 \) each
Finding Averages
\( 4{,}560 \) total points \( \div 12 \) games

The Division Relationship

Dividend
\(=\)
 Divisor
\(\times\)
 Quotient
\(+\)
\(R\)
 what you split groups of per group

The Standard Algorithm: Four Repeating Steps

1
Divide: How many times does the divisor go into the current portion of the dividend?
2
Multiply: Multiply the divisor by that partial quotient digit.
3
Subtract: Subtract the product from the current portion.
4
Bring down: Bring down the next digit of the dividend. Then repeat from step 1.

Short vs Long Division

Short Division Long Division
Divisor size 1-digit Any number of digits
Written work Remainders kept in head All steps written out
Best for Quick mental checks Multi-digit divisors
Example \( 945 \div 3 \) \( 7{,}854 \div 26 \)

How to Apply the Algorithm

1
Set up the problem with the division bracket. Write the dividend inside and the divisor outside.
2
Look at the leftmost digits of the dividend. Find the smallest group of digits the divisor fits into.
3
Divide, Multiply, Subtract, Bring Down. Write the quotient digit on top, aligned over the last digit you used.
4
Repeat until no digits remain to bring down.
5
Check: Multiply \( \text{quotient} \times \text{divisor} + \text{remainder} \) and verify it equals the dividend.

Example 1: \( 936 \div 4 \)

\(4\)
\(9\)
\(3\)
\(6\)
\(2\)
\(3\)
\(4\)
\(8\)
\(1\)
\(3\)
\(1\)
\(2\)
\(1\)
\(6\)
\(1\)
\(6\)
\(0\)
 Dividend: 936 Divisor: 4 Quotient: 234 Remainder: 0

Example 2: \( 1{,}575 \div 6 \)

\(6\)
\(1\)
\(5\)
\(7\)
\(5\)
\(2\)
\(6\)
\(2\)
\(1\)
\(2\)
\(3\)
\(7\)
\(3\)
\(6\)
\(1\)
\(5\)
\(1\)
\(2\)
\(3\)
 Dividend: 1,575 Divisor: 6 Quotient: 262 Remainder: 3

Example 3: \( 4{,}368 \div 14 \)

\(14\)
\(4\)
\(3\)
\(6\)
\(8\)
\(3\)
\(1\)
\(2\)
\(4\)
\(2\)
\(1\)
\(6\)
\(1\)
\(4\)
\(2\)
\(8\)
\(2\)
\(8\)
\(0\)
 14 doesn't fit into 4, so look at 43 first. Bring down the 6. Bring down the 8. Answer: 312

Tricky Case: Zeros in the Quotient

Sometimes the divisor doesn't fit into the current number after a bring-down. When that happens, write a zero in the quotient and bring down the next digit.

\(5\)
\(5\)
\(0\)
\(3\)
\(5\)
\(1\)
\(0\)
\(0\)
\(7\)
\(5\)
\(0\)
\(0\)
\(0\)
\(0\)
\(3\)
\(0\)
\(3\)
\(5\)
\(3\)
\(5\)
 5 can't go into 0 : write 0 in quotient! Answer: 1,007

Place Value Alignment Is Everything

Each quotient digit must line up directly above the last digit of the portion you're dividing. Misaligned digits lead to answers that are 10 times too big or too small.

✓ Correct H T O
\(2\)
\(3\)
\(4\)
\(4\)
\(9\)
\(3\)
\(6\)
 ✕ Wrong H T O
\(2\)
\(3\)
\(4\)
\(4\)
\(9\)
\(3\)
\(6\)
 Shifted left: answer looks like 2,340!

Estimating Quotient Digits

With a 2-digit divisor, you may not instantly know the quotient digit. Estimate by rounding the divisor and using mental math, then adjust.

1
Round the divisor to the nearest ten. For \(14\), think \(10\) or \(15\).
2
Estimate: How many times does the rounded divisor go in? If the portion is \(43\) and the divisor is \(14 \approx 15\), try \(2\) or \(3\).
3
Test it: Multiply and see if the product is less than or equal to the portion. If too big, go one lower. If there's room for more, go one higher.

Example 4: \( 8{,}645 \div 23 \)

1
\(23\) into \(8\)? Too small. Look at \(86\). Estimate: \(23 \times 3 = 69\), \(23 \times 4 = 92\). So the first digit is \(3\). Subtract: \(86 - 69 = 17\).
2
Bring down \(4 \to 174\). \(23 \times 7 = 161\), \(23 \times 8 = 184\). Digit is \(7\). Subtract: \(174 - 161 = 13\).
3
Bring down \(5 \to 135\). \(23 \times 5 = 115\), \(23 \times 6 = 138\). Digit is \(5\). Subtract: \(135 - 115 = 20\).

Common Mistakes to Avoid

✕ Forgetting the Zero
When the divisor doesn't fit, you must place a 0 in the quotient. Skipping it causes a significant place value error.
✕ Misaligned Digits
Each quotient digit must sit directly above the last digit of the group you divided into.
✕ Subtraction Errors
A small subtraction mistake cascades through every remaining step. Double-check each subtraction.

Summary: The Algorithm at a Glance

Step Action Watch For
Divide How many times does divisor fit? Estimate, then test
Multiply Divisor \(\times\) quotient digit Must be \(\leq\) current portion
Subtract Portion \(-\) product Borrow carefully
Bring Down Next digit joins remainder Place value alignment
Check \(Q \times D + R = \text{Dividend}\) Catches all errors

Question 1 of 5

What is \( 7{,}256 \div 8 \)?

Question 2 of 5

What is the remainder when you divide \( 4{,}597 \div 6 \)?

Question 3 of 5

What is \( 9{,}108 \div 12 \)?

Question 4 of 5

A student divides \( 6{,}030 \div 5 \) and gets \( 126 \). What did they likely do wrong?

Question 5 of 5

A class of 18 students earned a combined \( 1{,}674 \) points. How many points per student?