Factors

What are the Factors of 216? | Prime Factorization of 216

Written by Prerit Jain

Updated on: 12 Aug 2023

What are the Factors of 216? | Prime Factorization of 216

The factors of 216 are the numbers that will give a result of 216 (original product) when two numbers are multiplied together. These pairs of numbers can be either negative or positive. They can also be in fractions or decimal numbers as well. We provided you with three mathematical methods to find the factors of 216.

The factor tree method, the prime factorization method, and the division method are the three methods that you are going to learn in this article.

What are the Factors of 216

The factors of 216 are the numbers that will be divided by 216 exactly without a remainder being left. Moreover, they are also the numbers, that will give the original number after being multiplied in the pairs. Since 216 is a composite number, it has more than 2 factors, and here are the factors of 216:

Write Factors of 216 in Pairs

A pair of 216 factors is a combination of two numbers when multiplied together will give the result 216 which is an original product. They can either be a positive or negative pair. Here are the positive and negative pairs of 216. Here are the pairs:

Positive Pair Factors of 216

So, the positive pairs for 216 are (1, 216), (2, 108), (3, 72), (4, 54), (6, 36), (8, 27), (9, 24), and (12, 18).

Negative Pair Factors of 216

So, the negative pairs for 216 are (-1, -216), (-2, -108), (-3, -72), (-4, -54), (-6, -36), (-8, -27), (-9, -24), and (-12, -18).

How To Find Factors of 216 Through Division Method?

You can find factors of 216 through the division method. In this method, you have to divide 216 by a sequence of natural numbers to find the factors of 216. For your better understanding, we have explained the steps below.

• 216 ÷ 1 = 216
• 216 ÷ 2 = 108
• 216 ÷ 3 = 72
• 216 ÷ 4 = 54
• 216 ÷ 6 = 36
• 216 ÷ 8 = 27
• 216 ÷ 9 = 24
• 216 ÷ 12 = 18
• 216 ÷ 18 = 12
• 216 ÷ 24 = 9
• 216 ÷ 27 = 8
• 216 ÷ 36 = 6
• 216 ÷ 54 = 4
• 216 ÷ 72 = 3
• 216 ÷ 108 = 2
• 216 ÷ 216 = 1

Hence, after division, we can see that 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216 are the factors of 216 through the division method.

Prime Factorization of 216?

As 216 is a composite number, it has a lot of prime numbers. We can find factors of 216 through this method. Let’s see the method step by step:

As we have reached 1 and we cannot divide it anymore, we will stop and write down all the prime factors. The prime factors of 216 are 2 X 2 X 2 X 3 X 3 X 3 or 23 X 33. We can also write it down as 2 and 3 as both of them are prime numbers of 216. You can also see the image below for reference:

Write the Factor Tree of 216

Students can also use the factor tree to find the prime factors of 216. In a factor tree, we will divide the number until the answer becomes 1, and the factors are written in the form of branches of a tree. Then, the last factors are circled, and they are the prime factors of the number. The detailed steps on how to do this are explained below:

Circling all the branches, 2 X 2 X 2 X 3 X 3 X 3 or 23 X 33 = 216, which are prime factors of 216. Below is a picture for reference:

Solved Examples of Factors of 216

Here are some solved examples for students.

What is the sum of all the factors of 216?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216 are the 216 factors of 216.
1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 27 + 36 + 54 + 72 + 108 + 216 = 600
Hence, 600 is the sum of all factors of 216.

What are the factors and prime factors of 216?
Factors of 216: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
Prime Factors of 216: 2 X 2 X 2 X 3 X 3 X 3 or 22 X 33.

What’s the highest common factor between 90 and 216?
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
Hence, from the above, the common factor of 90 and 216 is 1, 2, 3, 6, 9, and 18.
The highest common factor between 90 and 216 is 18.

What’s the highest common factor between 150 and 216?
The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
Hence, from the above, the common factor of 150 and 216 is 1, 2, 3, and 6.
The highest common factor between 150 and 216 is 6.

Is 72 a factor of 216?
Yes, 72 is a factor of 216.
As 216 ÷ 3 = 72.

Is 20 a factor of 216?
No, 20 is not a factor of 216.
As 216 ÷ 20 = leaves a remainder.

FAQs

List all the factors of 216.
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216 are factors of 216.

What’s the highest common factor between 12 and 216?
The highest common factor between 12 and 216 is 12.

How many factors of 216 are also factors of 12?
The common factor of 12 and 216 is 1, 2, 4, and 12.

What are the composite factors of 216?
6, 8, 9, 12, 12, 24, 27, 36, 54, 72, 108, and 216 are the composite factors of 216.

What are the factors of 216 in pairs?
(1, 216), (2, 108), (3, 72), (4, 54), (6, 36), (8, 27), (9, 24), and (12, 18) are the factors of 216 in pairs.

What are the first 5 factors of 216?
1, 2, 3, 4, and 6 are the first 5 factors of 216.

What are the negative factors for 216?
-1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -27, -36, -54, -72, -108, and -216 are the negative factors of 216.

So, that’s all for factors of 216, prime factorization, and some solved examples for you. We hope this has been useful and clear.

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Prerit Jain

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