Factors of 18

What are the factors of 18? What is the factorization of 18?

What are the factors of 18?

In mathematics, the term factor refers to any number that divides evenly into another number with zero as a remainder.

What is a factor of 18?

• 3 is a factor of 6 because 6 ÷ 3 = 2 → the remainder is zero

• 5 is not a factor of 6 because 6 ÷ 5 = 1.2 → since the result is a decimal, the remainder is not zero

Whenever you have to find the factors of a number like 18, your strategy will be to use division to find the complete list of numbers that evenly divide into 18 without a remainder (i.e. the result is not a decimal).

The strategy of finding the factors of any number (the factors of 18 in this case) is illustrated in Figure 01 below.

What is a factor of 18? Let’s take a look at an example of a factor of 18 and an example of a non-factor of 18.

• 9 is a factor of 18 because 18 ÷ 9 = 2 → the remainder is zero

• 10 is not a factor of 18 because 18 ÷ 10 = 1.8 → since the result is a decimal, the remainder is not zero

Finding All Factors of 18

To find all factors of 18 (or any other number), you will follow the same process of using division to see which whole numbers evenly divide into 18 with out a remainder.

The best way to find all factors of 18 is to start by dividing 18 by 1 and then follow along with 2, 3, 4, 5, 6, 7, etc. Any numbers that can be divided into 18 evenly without a remainder will be on the list of factors of 18.

*Know that the number 1 will always be a factor of any number because 1 divides evenly into any number without a remainder, so any list of factors for any number will include 1.

**Also, the number that you are searching for the factors of will also always be a factor (in this case, 18) , since any number divided by itself equals 1 (with no remainder).

Therefore, you already know two of the factors of 18: 1 and 18

Now, you continue on finding all of the factors of 18. The value table in Figure 02 below demonstrates what the process of finding which numbers from 1-10 are factors of 18.

From the chart, you can see that the only whole numbers between 1 and 10 that evenly divide into 18 with no remainder are 1, 2, 3, 6, and 9, so these numbers are all factors of 18.

By continuing this process, you will find one additional factor of 18.

• 18 is a factor of 18 because 18 ÷ 18 = 1 → no remainder

So, you can conclude that all of the factors of 18 are 1, 2, 3, 6, 9, and 18

Prime Factorization of 18

Next, we will explore what is the prime factorization of 18.

Prime factorization is a math term that refers to finding the prime numbers that can be multiplied together resulting in the original number. The prime factorization process requires you to express the original number as a product of its prime factors.

It is important to note that prime factors are numbers that are both factors of a number AND also prime. So, finding the prime factors of a number is more specific than just finding the factors.

As a reference, all of the prime numbers between one and fifty are displayed in Figure 04.

The simplest method for finding the prime factorization of 18 is to make a factor tree that breaks down 18 based on its prime factors.

The completed factor tree for the factorization of 18 is shown in Figure 05 below.

So, we can conclude that the prime factorization of 18 is:

• 18 = 2 × 3 × 3

That’s all there is to it! We have just completed determining all of the factors of 18 as well as the prime factorization of 18. You can repeat both processes to finding the factors and prime factorization of any number, so, if you are still confused with factoring, we recommend going back and working through this guide again.

Keep Learning:

• What are the factors of 27?

• What are the factors of 30?

• What are the factors of 63?

• What are the factors of 147?

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