Factors of 16 | Prime Factorization and Division Method

Factors of 16

Factors of 16 represent the numbers that produce 16 when multiplied by two numbers. 

For example: 

(1,16) and (-1,-16) are the pair factors of 16. If we multiply a pair of negative factors, the result should be the original number. For example, if we multiply -1 × -16, we get 16. 

As we use different methods to find the factors of any number, similarly, I will use the factorization method to determine the factors of the number 16.

In this article, we will discover the prime factors of 16 and the pair factors with complete explanations.

What are the Factors of 16?

The factors of 16 are numbers that divide 16 completely without leaving a remainder. Since 16 is a composite number, it has more than one factor. 

Among the factors of 16 are 1, 2, 4, 8, and 16. 

As well, 16 has negative factors -1, -2, -4, -8, and 16.

What are the Factors of -16?

When we multiply two numbers, and we get -16 as a product, those numbers are the factors of -16. 

Here is the explanation:

-1 × 16 = -16

 1 × -16 = -16

 -2 × 8 = -16

 2 × -8 = -16

 -4 × 4 = -16

 4 × -4 = -16

We can get -16 by having (-1, 16), (-2, 8), and(-4, 4) as a pair of factors. Similarly, we can also get -16 by having (1, -16), (2, -8), and(4, -4) as a pair of factors.

Pair Factors of 16

In order to find the pair factors of 16, multiply each number in a pair by the original number to get 16; such numbers are shown below:

How to calculate the Factors of 16?

Follow these steps to calculate the factors of 16.

• The first number you should write is 16.
• Choose two numbers that produce 16 when multiplied, such as 2 and 8, such as 2 × 8 = 16.
• There are only two factors in the prime number 2, namely 1, and the number itself (1 and 2). Therefore, it cannot be further factorized.

• Consider the number 8, which is not a prime number, but a composite number. As a result, it is further factorizable.
• You can factor 8 as 2 × 2 × 2 × 1.
• Therefore, 16 can be factorized as 2 × 2 × 2 × 2 × 1.

Prime Factors of 16 By Division Method

In order for the number 16 to be composite, it must have prime factors. Let’s see how you can find the prime factors of 16.

• As a first step, divide 16 by the smallest prime number, say 2.
• 16 ÷ 2 = 8

• The process is repeated by dividing 8 by 2.
• 8 ÷ 2 = 4
• 4 ÷ 2 = 2
• 2 ÷ 2 = 1

After the division process, we received the number 1. Therefore, we cannot continue. Thus, the prime factors of 16 are written as 2 × 2 × 2 x 2 or 24, where 2 is a prime number.

Solved Examples

Example 1:

Calculate the common factor of 16 and 24.

Solution:

The factors of 16 are 1, 2, 4, 8, and 16.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

Therefore, the common factor of 24 and 16 is 1, 2, 4, and 8.

Example 2:

What is the sum of the factors of 16?

Solution:

As we know, the factors of 16 are 1, 2, 4, 8, and 16.

Therefore, the sum of the factors of 16 is 1+2+4+8+16.

The sum of 16 factors is 31

Example 3:

Find out the common factors of 16 and 47.

Solution:

Factors of 16 = 1, 2, 4, 8 and 16

Factors of 47 = 1, and 47.

Therefore, the common factor of 47 and 16 is 1.

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