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Long Division – Definition, Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Long DivisionLong Division – Definition, ExamplesTable of ContentsLong Division Definition of Long Division

Long division is a mathematical method used to divide large numbers into smaller groups or parts. It breaks down complex division problems into simple, manageable steps. In long division, we work with four main components: the dividend (the number being divided), the divisor (the number we divide by), the quotient (the result of division), and the remainder (the leftover amount that cannot be divided further).

When performing long division, we can use the division symbol "÷÷÷" between numbers, or express it as a fraction. For example, 36 divided by 6 can be written as 36÷636 ÷ 636÷6 or as 366\frac{36}{6}636​. Long division can be used with both whole numbers and decimals. When working with decimals, we follow the same steps as with whole numbers: divide, multiply, subtract, bring down, and repeat until we find the final quotient and remainder.

Examples of Long Division Example 1: Basic Long Division with a Remainder Problem:

Divide 726 by 4

Step-by-step solution: Step 1, Divide 7 by 4: 4 goes into 7 once with remainder 3. Write 1 in the quotient.

Divide 726 by 4

Step 2, Bring down 2 to get 32. Divide 32 by 4: 4 goes into 32 eight times. Write 8 in the quotient.

Divide 726 by 4

Step 3, Bring down 6 to get 6. Divide 6 by 4: 4 goes into 6 once with remainder 2. Write 1 in the quotient.

Divide 726 by 4

Step 4, So, the quotient is 181 with a remainder of 2. Example 2: Long Division with No Remainder Problem:

What is the remainder when we divide 248 by 8?

Step-by-step solution: Step 1, 8 cannot go into 2, so look at 24. 8 goes into 24 three times. Write 3 in the quotient.

Divide 248 by 8

Step 2, Multiply and subtract: 3×8=243 × 8 = 243×8=24. 24−24=024 - 24 = 024−24=0. Bring down 8 to get 8.

Divide 248 by 8

Step 3, Divide 8 by 8: 8 goes into 8 exactly once. Write 1 in the quotient.

Divide 248 by 8

Step 4, Multiply and subtract: 1×8=81 × 8 = 81×8=8. 8−8=08 - 8 = 08−8=0. Nothing remains.

Divide 248 by 8

The quotient is 31 with a remainder of 0.

Example 3: Long Division with Decimals Problem:

Divide 56.7 by 9

Step-by-step solution: Step 1, 9 cannot go into 5, so look at 56. 9 goes into 56 six times. Write 6 in the quotient.

Divide 56.7 by 9

Step 2, Multiply and subtract: 6×9=546 × 9 = 546×9=54. 56−54=256 - 54 = 256−54=2. Bring down 7 to get 27.

Divide 56.7 by 9

Step 3, Divide 27 by 9: 9 goes into 27 exactly three times. Write 3 in the quotient.

Divide 56.7 by 9

Step 4, Multiply and subtract: 3×9=273 × 9 = 273×9=27. 27−27=027 - 27 = 027−27=0. Nothing remains.

Divide 56.7 by 9

The quotient is 6.3.

Comments(6)RResearcherJakeNovember 6, 2025I've been struggling to explain long division to my students. This page's def and examples made it super easy! Thanks for the great resource.

NNatureLover75September 17, 2025I’ve been struggling to explain long division to my kids, but this page breaks it down so well! The examples with remainders and decimals were super helpful. Definitely bookmarking this for homework time!

SSunnyTravelerSeptember 10, 2025I’ve been struggling to explain long division to my 4th grader, but this page broke it down so clearly! The step-by-step examples really helped us both. Thanks for making math less stressful!

MCMs. CarterAugust 27, 2025I’ve been struggling to explain long division to my 4th grader, but this page made it so easy! The step-by-step examples were a lifesaver. We especially liked the word problems—it’s great for practice!

NNatureLover42August 20, 2025This page was a lifesaver! I used the clear steps and examples to help my daughter finally understand long division. The word problems were especially helpful for making it click!

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