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Factors, GCF, LCM & Division • Lesson 18 ⏱ 6 min read 📅 Updated Nov 2026

Long Division Step-by-Step: Quotient, Remainder, and Decimals

Master long division with the DMSB mnemonic (Divide, Multiply, Subtract, Bring down), handling remainders and continuing into decimal fractions.

Step-by-Step Algorithm

Long division breaks down a big division into easy cycles of 4 steps: Divide → Multiply → Subtract → Bring Down (DMSB).

64 ← Quotient (Roof) 4 257 Remainder = 1 (Answer: 64 R1 or 64.25)
Long Division Anatomy: Divisor (Outside) • Dividend (Inside) • Quotient (Top)

The 4 Components of Division

TermRoleWhere It SitsExample (257 ÷ 4)
DividendThe total amount to splitInside the division house257
DivisorNumber of groupsOutside on the left4
QuotientThe whole answerOn the roof (top)64
RemainderWhat is left overAt the very bottom1 (or 64 1/4 = 64.25)
Try It Yourself

Practice with Our Interactive Long Division Calculator

Check your calculations or explore full step-by-step solutions instantly.

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Solved Step-by-Step Examples:100 ÷ 7 (Quotient & Remainder)250 ÷ 4500 ÷ 8
Your Turn!

Check Your Understanding (3 Quick Questions)

Score: 0 / 3

Question 1: In 100 ÷ 7 = 14 R 2, what is 14 called?

Question 2: What is the 4-step long division sequence?

Question 3: How can 17 ÷ 5 be written as a mixed number?