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Divisor: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">DivisorDivisor: Definition and ExampleTable of ContentsDefinition of Divisor

In mathematics, a divisor is a number that divides another number, either completely or partially. When performing division, the divisor is the number by which we divide the dividend to obtain the quotient. For example, in the expression 20÷5=420 \div 5 = 420÷5=4, the number 555 is the divisor, 202020 is the dividend, and 444 is the quotient. The divisor determines how many equal parts or groups the dividend will be divided into, essentially indicating the size or magnitude of each resulting part or group.

Divisors follow several important properties that help us understand their behavior in mathematical operations. First, zero can never be a divisor because division by zero is undefined. When the divisor is 111, the quotient equals the dividend (e.g., 65÷1=6565 \div 1 = 6565÷1=65). Similarly, when the dividend equals the divisor, the quotient is always 111 (e.g., 65÷65=165 \div 65 = 165÷65=1). An important rule to remember is that the remainder in any division problem is always less than the divisor. Additionally, a factor is a special case of a divisor where the remainder equals zero.

Examples of Divisors in Mathematics Example 1: Identifying Parts of Division Problem:

Identify the dividend and divisor in each division problem.

i) 108÷12108 \div 12108÷12 ii) 24÷524 \div 524÷5 iii) 200÷10200 \div 10200÷10 iv) 7÷27 \div 27÷2 Step-by-step solution:

Step 1, Recall that in a division problem, the dividend is the number being divided and the divisor is the number by which we divide the dividend.

Step 2, For part i) 108÷12108 \div 12108÷12:

The dividend is 108108108 (the number being divided) The divisor is 121212 (the number we're dividing by)

Step 3, For part ii) 24÷524 \div 524÷5:

The dividend is 242424 (the number being divided) The divisor is 555 (the number we're dividing by)

Step 4, For part iii) 200÷10200 \div 10200÷10:

The dividend is 200200200 (the number being divided) The divisor is 101010 (the number we're dividing by)

Step 5, For part iv) 7÷27 \div 27÷2:

The dividend is 777 (the number being divided) The divisor is 222 (the number we're dividing by) Example 2: Finding All Parts of a Division Problem Problem:

Define the parts of division when 729729729 is divided by 999.

Step-by-step solution:

Step 1, Identify the dividend and divisor.

Dividend = 729729729 (the number being divided) Divisor = 999 (the number we're dividing by)

Step 2, Perform the division operation to find the quotient.

To divide 729729729 by 999, we can break it down: 999 goes into 777 zero times, with 777 remaining 999 goes into 727272 eight times, with 000 remaining 999 goes into 999 one time, with 000 remaining So 729÷9=81729 \div 9 = 81729÷9=81

Step 3, Determine the remainder.

Since 999 divides 729729729 evenly, the remainder is 000.

Step 4, Verify the answer using the division formula.

Dividend = (Divisor × Quotient) + Remainder 729=(9×81)+0729 = (9 \times 81) + 0729=(9×81)+0 729=729+0729 = 729 + 0729=729+0 729=729729 = 729729=729 ✓ Example 3: Applying Division in a Real-World Context Problem:

Alex distributed 121212 strawberries equally. Everybody got only 111 strawberry. What is the divisor and what does the divisor represent?

Step-by-step solution:

Step 1, Identify what we know.

Total number of strawberries (dividend) = 121212 Number of strawberries each person received (quotient) = 111

Step 2, Determine the divisor using the relationship between dividend, divisor, and quotient.

In this problem, the divisor represents the number of people who received strawberries. Using the formula: Dividend ÷ Divisor = Quotient 12÷Divisor=112 \div \text{Divisor} = 112÷Divisor=1 Solving for Divisor: Divisor=12÷1=12\text{Divisor} = 12 \div 1 = 12Divisor=12÷1=12

Step 3, Interpret what the divisor means in this context.

The divisor, which equals 121212, represents the number of people who received strawberries. Alex divided the 121212 strawberries equally among 121212 people, giving each person exactly 111 strawberry.

Step 4, Verify the answer.

If each of the 121212 people gets 111 strawberry, then the total number of strawberries distributed would be 12×1=1212 \times 1 = 1212×1=12, which matches our original number of strawberries. Comments(9)SSportsTutorLanaNovember 6, 2025I've used this divisor definition with my students. It's super clear! Really helped them grasp the concept and solve related problems.

SSkierYvonneNovember 5, 2025This divisor def is great! I've used it to explain to my students. It made the concept easy for them to grasp. Thanks!

YYogiAriaNovember 5, 2025This divisor definition is great! I've used it to explain to my students, and it really helped them grasp the concept. Thanks!

BBookLover85September 17, 2025I’ve used the divisor definition and examples from this page to help my kids with their math homework. It’s clear and easy to follow, plus the examples really make the concept click!

MCMs. CarterSeptember 9, 2025I used the clear definition and examples here to help my kids understand divisors for their math homework. It’s such a simple breakdown, and the examples made all the difference!

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