Arithmetic consists of addition, subtraction, multiplication and division. Out of these four basic operations of math, many students find division the hardest.

While division can be explained in its simplest form as the act of splitting a number (or object) into separate parts, things get dramatically more complicated the deeper you delve into the topic. If you’ve ever tried to do long division or divide a fraction or a decimal number, you’ll know what we mean.

Plus, from “integers” to “divisors”, there’s so much terminology to wrap your get around, it can be a struggle to understand what question you’re being asked. So, in this article, we’re going to clear things up by explaining what some of this terminology means, focusing mainly on the definition of the word “divisor”.

A divisor can be defined as any number that divides another number — either completely or with a remainder. For example, in the equation 20 ÷ 4 = 5, the divisor is 4.

When solving division problems, it’s also important to know that the number being divided is called the dividend, and the answer is known as the quotient. So, for the example given above, the dividend is 20, and the quotient is 5.

Continue reading to find out more about divisors and the definitions of some of the other division terms.

### What does the divisor look like in an equation?

Division can be written out in various ways. This means the divisor will be in a different place, according to the method used.

The most commonly used division symbol is the obelus, which looks like this: ÷. Equations that use this divide symbol put the divisor in between the dividend and the quotient. For example:

20 ÷ 4 = 5

A slash (“/”) can also be used to represent division. As with using the obelus, the divisor is in the middle. For example:

20 / 4 = 5

Division can also be depicted with a horizontal bar, which is known as a “fraction bar”. In this case, again the dividend comes first, but the divisor is below it, with the quotient to the right. For example:

20

— = 5

4

For more complicated division questions, the division bar is used. It looks like this: 厂. This time, the divisor is to the left, with the dividend to the right and the quotient on the top. For example:

5

4厂20

### What are the properties of a divisor?

As with the other three arithmetic operations, division follows certain rules. Because of these rules, a divisor will have the following interesting properties:

• If both the divisor and the dividend are whole numbers, it doesn’t necessarily mean that the quotient will be a whole number.
• If the divisor has the same value as the dividend, the quotient will always be 1.
• If the divisor is a decimal number, it cannot be divided until it is converted to a whole number.
• The quotient cannot be changed by multiplying the divisor and the dividend by the same number.
• The value of the divisor can never be zero. This is because dividing something into zero parts doesn’t make sense.
• While a divisor can be either a positive or a negative number, the term “divisor” refers to a positive divisor unless stated otherwise.

### What is a factor?

A factor is a type of divisor. If a divisor goes into a dividend an exact number of times, leaving no remainder, then it is a factor.

So, in our 20 ÷ 4 = 5 example, both 4 and 5 are factors of 20, because they divide 20 entirely.

It’s important to remember that all factors are divisors, but not all divisors will be factors. Take the number 7, for example. It can’t be divided into 20 exactly, so it is not a factor of 20. However, it is a factor of 21. In fact, 21 has four factors: 1, 3, 7 and 21. These are the numbers that divide 21 an exact number of times, with nothing left over.

Because division and multiplication are inverse operations (which means one can be used to undo the other), you can use multiplication to check your answer to a division problem.

While the dividend divided by the divisor equals the quotient, the divisor multiplied by the quotient equals the dividend.

So, you can check that 20 ÷ 4 = 5 is correct with the equation 4 x 5 = 20. Checking the answers to multiplication problems can be done in the same way.

### Glossary of division terms

In order to understand a division question, you need to be familiar with the following terms:

• Dividend — The dividend is the number that is to be divided, or split up, into a number of different parts. For example, in the equation 20 ÷ 4 = 5, the dividend is 20.
• Divisor The divisor is the number that divides the dividend. For example, in the equation 20 ÷ 4 = 5, the divisor is 4.
• Factor — A factor is a divisor that leaves no remainder.
• Integer — An integer is a whole number. The number 5, for example, is an integer, while 5.5 is not.
• Partitive — Also known as “partition”, this is a type of division that considers the size of the parts that make up the whole.
• Prime numbers — These are whole numbers that can only be divided by 1 and themselves. Some examples of prime numbers are 2, 5, 7, 11, 13, 17, 19, 23 and 29.
• Composite numbers — These are whole numbers that can be divided by more than just 1 and themselves. Some examples of composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28 and 30.
• Quotient — The quotient is the answer to a division question. For example, in the equation 20 ÷ 4 = 5, the quotient is 5.
• Quotition — This is a type of division that considers how many parts make up the whole.
• Remainder — The remainder is the amount leftover after a calculation has been completed. There will only be a remainder if the divisor doesn’t go into the dividend exactly.

### Summary

A divisor can be defined as any number that divides another number — either completely or with a remainder. When studying division, some of the most important terms to understand are dividend, divisor and quotient. These terms can be defined using the following example: 20 ÷ 4 = 5. In this case, the dividend is 20, the divisor is 4 and the quotient is 5. It’s also important for arithmetic students to know what a factor is. A factor is a divisor that goes into a dividend an exact number of times, leaving no remainder.

A divisor has many interesting properties. Some examples of these are:

• If the divisor has the same value as the dividend, the quotient will always be 1
• The quotient cannot be changed by multiplying the divisor and the dividend by the same number
• The value of the divisor can never be zero because dividing something into zero parts doesn’t make sense