Factors of 216

The factors of 216 are the numbers, that produce the result as 216 when two numbers are multiplied together. Consider an example, the factor pairs of 89 is written as (1, 89) and (-1,-89). When we multiply the pair of negative factors, the result should give the original number, such as multiplying -1 × -89, then we get the number 89. Thus, we can consider both positive and negative factor pairs of 89. Factor pairs of the number 216 are the whole numbers which could be either positive or negative but not a fraction or decimal number. To find the factors of a number, 216, we will use the factorization method.

In the factorization method, first take the numbers, 1 and 216 as factors of 216 and proceed with finding the other pair of multiples of 216 which gives the results as an original number. To understand this method in a better way, read the article below to find factor 216 in pairs and also the division method to find the prime factors of 216 is discussed.

Table of Contents:

• What are the Factors of 216?
• Pair Factors of 216
• How to Find the Prime Factors of 216?
• Prime Factorization of 216
• Solved Examples
• FAQs

What are the Factors of 216?

The factors of 216 are the numbers that divide the number 216 exactly without leaving the remainder. In other words, the factors of 216 are the number, which when multiplied in pairs gives the original number 216. As 216 is the composite number, it has more than two factors. Thus, the factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108 and 216.

Pair Factors of 216

To find the pair factors of 216, multiply the two numbers in a pair to get the original number as 216, such numbers are as follows

If 1 × 216 = 216, then (1, 216) is a pair factor of 216.

Similarly,

2 × 108 = 216, (2, 108) is a pair factor of 216

3 × 72 = 216, (3, 72) is a pair factor of 216

4 × 54 = 216, (4, 54) is a pair factor of 216

6 × 36 = 216, (6, 36) is a pair factor of 216

8 × 27 = 216, (8, 27) is a pair factor of 216

9 × 24 = 216, (9, 24) is a pair factor of 216

12 × 18 = 216, (12, 18) is a pair factor of 216

Therefore, the positive pair factors of 216 are (1, 216), (2, 108), (3, 72), (4, 54), (6, 36), (8, 27), (9, 24), and (12, 18)

To find the negative pair factors of 216, then proceed with the following steps:

If -1 × -216 = 216, then (-1, -216) is a pair factor of 216.

Similarly,

-2 × -108 = 216, (-2, -108) is a pair factor of 216

-3 × -72 = 216, (-3, -72) is a pair factor of 216

-4 × -54 = 216, (-4, -54) is a pair factor of 216

-6 × -36 = 216, (-6, -36) is a pair factor of 216

-8 × -27 = 216, (-8, -27) is a pair factor of 216

-9 × -24 = 216, (-9, -24) is a pair factor of 216

-12 × -18 = 216, (-12, -18) is a pair factor of 216

Therefore, the negative pair factors of 216 are (-1, -216),(-2, -108), (-3, -72), (-4, -54), (-6, -36), (-8, -27), (-9, -24), and (-12, -18)

How to calculate the Prime Factors of 216?

Learn the following steps to calculate the factors of 216.

• • First, write the number 216
  • Find the two numbers, which gives the result as 216 under the multiplication, say 2 and 108, such as 2 × 108 = 216.
  • We know that 2 is a prime number that has only two factors, i.e., 1 and the number itself (1 and 2) which cannot be further factorized. (i.e.) 2 = 2 × 1

• • But look at the number 108, which is a composite number but not a prime number and it can be further factorized. 108 can be factored as 2 × 2 × 3 × 3 × 3× 1
  • Therefore, the factorization of 216 is written as, 216 = 2× 2 × 2× 3 × 3 × 3 × 1
  • Finally, write down all the unique numbers that are obtained as factors.

Prime Factorization of 216

The number 216 is a composite and it should have prime factors. Now let us know how to calculate the prime factors of 216.

Step 1: The first step is to divide the number 216 with the smallest prime factor, say 2.

216 ÷ 2 = 108

Step 2: Again divide 108 by 2 and the process goes on.

108 ÷ 2 = 54

54 ÷ 2 = 27

Step 3: You will get a fractional number if you divide 27 by 2. Thus, continue with the next prime factor, 3

27 ÷ 3 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

Finally, we received the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors of 216 are written as 2 × 2 × 2 × 3 × 3 × 3 or 2³ × 3³, where 2 and 3 are the prime numbers.

It is possible to find the exact number of factors of a number 216 with the help of prime factorisation. The prime factor of the 216 is 2³ × 3³. The exponents in the prime factorisation are 3 and 3. Add the number 1 with the exponents and multiply it. (3+1)(3+1) = 4 × 4 = 16. Therefore, the number 216 has 16 factors.

Video Lesson on Prime Factors

Solved Examples

Example 1:

Find the common factors of 216 and 215.

Solution:

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

The factors of 215 are 1, 5, 43 and 215

Therefore, the common factor of 216 and 215 is 1.

Example 2:

Find the common factors of 216 and 217.

Solution:

Factors of 216 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108 and 216.

Factors of 217 = 1, 7, 31 and 217.

Thus, the common factor of 216 and 217 is 1. 

Example 3:

Find the common factors of 216 and 116.

Solution: 

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

The factors of 116 are 1, 2, 4, 29, 58 and 116.

Therefore, the common factors of 216 and 116 are 1, 2 and 4.

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