Division

Long Division

2-Digit ÷ 1-Digit

Divide 78 ÷ 6 using long division. Work one digit at a time: divide 7 tens by 6, record quotient digit 1, multiply back and subtract to find the remainder, then bring down the 8 ones and repeat.

Example

Divide 78 by 6 using the long-division galley.

highlighted = computed this step

Step 1 — Set up

Set up the long-division galley.

x□□678\begin{array}{r|rr}\phantom{x}&\square&\square\\\hline\\6&7&8\end{array}
Set up 78 divided by 6.67dividend8dividend□quotient□quotientdividenot yetmultiplynot yetsubtractnot yetbring downnot yetdividenot yetmultiplynot yetsubtractnot yetcheck: 6 x 13 + 0 = 78

Step 2 — Write quotient digit

7 ÷ 6 = 1, write 1.

x1□678\begin{array}{r|rr}\phantom{x}&\hl{1}&\square\\\hline\\6&7&8\end{array}
Use the first digit: 7 ÷ 6 = 1.67dividend8dividend1quotient□quotientdivide7 ÷ 6 = 1multiplynot yetsubtractnot yetbring downnot yetdividenot yetmultiplynot yetsubtractnot yetcheck: 6 x 13 + 0 = 78

Step 3 — Multiply back

Multiply back: 1 x 6 = 6.

x1□678x6x\begin{array}{r|rr}\phantom{x}&1&\square\\\hline\\6&7&8\\\phantom{x}&\hl{6}&\phantom{x}\end{array}
Multiply back: 1 x 6 = 6.67dividend8dividend1quotient□quotient6divide7 ÷ 6 = 1multiply1 x 6 = 6subtractnot yetbring downnot yetdividenot yetmultiplynot yetsubtractnot yetcheck: 6 x 13 + 0 = 78

Step 4 — Subtract

Subtract: 7 - 6 = 1.

x1□678x6xx1x\begin{array}{r|rr}\phantom{x}&1&\square\\\hline\\6&7&8\\\phantom{x}&6&\phantom{x}\\\phantom{x}&\hl{1}&\phantom{x}\end{array}
Subtract: 7 - 6 = 1.67dividend8dividend1quotient□quotient61divide7 ÷ 6 = 1multiply1 x 6 = 6subtract7 - 6 = 1bring downnot yetdividenot yetmultiplynot yetsubtractnot yetcheck: 6 x 13 + 0 = 78

Step 5 — Bring down

Bring down the 8; the new working number is 18.

x1□678x6xx1x\begin{array}{r|rr}\phantom{x}&1&\square\\\hline\\6&7&\hl{8}\\\phantom{x}&6&\phantom{x}\\\phantom{x}&1&\phantom{x}\end{array}
Bring down 8: 1 and 8 make 18.67dividend8dividend1quotient□quotient61bring down 818divide7 ÷ 6 = 1multiply1 x 6 = 6subtract7 - 6 = 1bring down1 with 8 makes 18dividenot yetmultiplynot yetsubtractnot yetcheck: 6 x 13 + 0 = 78

Step 6 — Write quotient digit

18 ÷ 6 = 3, write 3.

x13678x6xx1x\begin{array}{r|rr}\phantom{x}&1&\hl{3}\\\hline\\6&7&8\\\phantom{x}&6&\phantom{x}\\\phantom{x}&1&\phantom{x}\end{array}
Now 18 ÷ 6 = 3.67dividend8dividend1quotient3quotient61bring down 818divide7 ÷ 6 = 1multiply1 x 6 = 6subtract7 - 6 = 1bring down1 with 8 makes 18divide18 ÷ 6 = 3multiplynot yetsubtractnot yetcheck: 6 x 13 + 0 = 78

Step 7 — Multiply back

Multiply back: 3 x 6 = 18.

x13678x6xx1xx18\begin{array}{r|rr}\phantom{x}&1&3\\\hline\\6&7&8\\\phantom{x}&6&\phantom{x}\\\phantom{x}&1&\phantom{x}\\\phantom{x}&\hl{1}&\hl{8}\end{array}
Multiply back: 3 x 6 = 18.67dividend8dividend1quotient3quotient61bring down 81818divide7 ÷ 6 = 1multiply1 x 6 = 6subtract7 - 6 = 1bring down1 with 8 makes 18divide18 ÷ 6 = 3multiply3 x 6 = 18subtractnot yetcheck: 6 x 13 + 0 = 78

Step 8 — Subtract

Subtract: 18 - 18 = 0.

x13678x6xx1xx18xx0\begin{array}{r|rr}\phantom{x}&1&3\\\hline\\6&7&8\\\phantom{x}&6&\phantom{x}\\\phantom{x}&1&\phantom{x}\\\phantom{x}&1&8\\\phantom{x}&\phantom{x}&\hl{0}\end{array}
Subtract: 18 - 18 = 0.67dividend8dividend1quotient3quotient61bring down 818180divide7 ÷ 6 = 1multiply1 x 6 = 6subtract7 - 6 = 1bring down1 with 8 makes 18divide18 ÷ 6 = 3multiply3 x 6 = 18subtract18 - 18 = 0check: 6 x 13 + 0 = 78

Step 9 — Result

Read the quotient 13 with remainder 0.

x13678x6xx1xx18xx0\begin{array}{r|rr}\phantom{x}&1&3\\\hline\\6&7&8\\\phantom{x}&6&\phantom{x}\\\phantom{x}&1&\phantom{x}\\\phantom{x}&1&8\\\phantom{x}&\phantom{x}&0\end{array}
Check: 6 x 13 + 0 = 78.67dividend8dividend1quotient3quotient61bring down 818180divide7 ÷ 6 = 1multiply1 x 6 = 6subtract7 - 6 = 1bring down1 with 8 makes 18divide18 ÷ 6 = 3multiply3 x 6 = 18subtract18 - 18 = 0check: 6 x 13 + 0 = 78
long-division-steps Long division processes one digit of the dividend at a time: estimate a quotient digit, multiply by the divisor, subtract, then bring down the next digit. Repeat until all digits are used.