Factors of 27

What are the factors of 27? What is the factorization of 27?

Any whole number that can be divided evenly into 27 without a remainder is a factor of 27.

Below you can find an instant answer to the question: what are the factors of 27? However, if you are looking for a step-by-step guide on how to find all factors of 27 (or any other number), move onto the sections below for a complete explanation, which will also show you how to find the prime factorization of 27.

▶ Factors of 27: 1, 3, 9, 27

▶ Prime Factorization of 27: 3 x 3 x 3

What are the factors of 27?

In math, a factor is any number that divides evenly into another number without any remainder.

For example:

• 7 is a factor of 14 because 14 ÷ 7 = 2 → no remainder

• 8 is not a factor of 14 because 14 ÷ 8 = 1.75 → there is a remainder (the result is a decimal)

Any time that you have to determine the factors of a number, you will be using division to determine whether or not a number is a factor as you create a list of factors. To do this, simply look for numbers that divide into 27 that results in a whole number (no remainder; result is not a decimal).

Determining the list of factors of any number (the factors of 27 in this case) is shown below in Figure 01.

What is a factor of 27? Below are two examples: one is an example of a factor of 27 and the other is example of a number that is not a factor of 27.

• 9 is a factor of 27 because 27 ÷ 3 = 9 → no remainder

• 10 is not a factor of 27 because 27 ÷ 10 = 2.7 → there is a remainder (the result is a decimal)

Finding All Factors of 27

You can determine all factors of 27 (or any other number) by following the process of using division to see which whole numbers divide into 27 without leaving a remainder.

The most simple method for finding all factors of 27 is to begin first by dividing 27 by 1 and then continue with the numbers 2, 3, 4, etc. Al of the numbers that can be divided into 27 without any remainder left over will be considered factors of 27.

*The number 1 will always be on the list of factors for any number. This is always true because the number 1 divides into any number without a remainder.

**Additionally, the original number (27 in this case) will also always be a factor because any number divided by itself is equal to 1, which is a whole number with no remainder.

So, you can already state that two of the factors of 27 are 1 and 27.

Next, you can continue finding the complete list of the factors of 27. In Figure 02 below, you will see a table that shows how you can determine which numbers between 1 and 10 (if any) are factors of 27.

By looking at the table, you can see that the only whole numbers between 1 and 10 that can be divided into 27 without any remainder are 1, 3, and 9, so these numbers are all factors of 27.

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

• 27 is a factor of 27 because 27 ÷ 27 = 1 → there is no remainder

So, you can conclude that all of the factors of 27 are 1, 3, 9, 27

Prime Factorization of 27

Now, we will learn how to determine the prime factorization of 27.

In math, finding the prime factorization of a number means finding prime numbers that, when multiplied together, result in the original number. The method of finding the prime factorization of 27 calls for you to express the original number, 27, as the product of its prime factors.

Note that prime factors are the numbers that are factors of 27 AND prime numbers too.

Figure 04 below shows a list of all of the prime numbers up to 50 for your reference.

The most straightforward method for finding the prime factorization of 27 is to draw a factor tree that breaks down the prime factors of 27.

The complete Prime Factorization of 27 factor tree is illustrated below in Figure 05.

Finally, we can conclude that the prime factorization of 27 is:

• 27 = 3 × 3 × 3

We have just successfully determined all the factors of 27 and the prime factorization of 27. The same steps can be followed to find the factors and prime factorization of any other number. If you still feel uncertain about finding the factors of a number of the prime factorization of a number, we suggest revisiting the examples in this guide and practicing the process further.

Keep Learning:

• What are the factors of 18?

• What are the factors of 30?

• What are the factors of 63?

• What are the factors of 147?

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