Factors of 16—with division and prime factorization

Factors of 16

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. 

We will use the factorization method to determine the factors of the number 16.

Factors of 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.

Factors of 16: 1, 2, 4, 8 and 16.Prime Factorization of 16: 2 × 2 × 2 × 2 or 24

 

What are Factors of -16?

When we multiply two numbers, and we get -16 as a product, that 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:

Positive Pair FactorsNegative Pair Factors
1 × 16 = 16 ⇒ (1, 16)-1 × -16 = 16 ⇒ (-1, -16)
2 × 8 = 16 ⇒ (2, 8)-2 × -8 = 16 ⇒ (-2, -8)
4 × 4 = 16 ⇒ (4, 4)-4 × -4 = 16 ⇒ (-4, -4)

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.
Factors of 16 by prime factorization

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.

Factors of 16 by division method
  • 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.

Links Related to Factors
Factors of 15= 1, 3, 5, and 15.Factor of 36= 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Factors of 48= 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.Factors of 18= 1, 2, 3, 6, 9, and 18.
Factors of 24=  1, 2, 3, 4, 6, 8, 12, and 24.Factors of 25= 1, 5, and 25.
Factors of 42= 1, 2, 3, 6, 7, 14, 21, and 42.Factors of 60= 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Factors of 35= 1, 5, 7, 35.Factors of 81= 1, 3, 9, 27, 81.
Factors of 75= 1, 3, 5, 15, 25 and 75.Factors of 56= 1, 2, 4, 7, 8, 14, 28 and 56.

Solved Examples

Example 1:

Calculate the common factor of 16 and 15.

Solution:

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

The factors of 15 = 1, 3, 5 and 15.

Therefore, the common factor of 15 and 16 is 1.

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 14.

Solution:

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

Factors of 14 = 1, 2, 7 and 14.

Therefore, the common factors of 14 and 16 are 1 and 2.

Factors of 14

FAQ’s

What are the multiples of 16?

Here is the list of 16 multiples:

16, 32, 48, 64, 80, 96, 112, 128, 144, 160, etc.

Are all factors of 16 even?

The other factors of 16 are all even numbers except 1. Therefore, factors of 16 are 1, 2, 4, 8, 16.

What are the prime factors for 16?

Prime factors of 16 as a product are 2 × 2 × 2 x 2 or 2^4, where 2 is the prime number.

What are the common factors of 12 and 16?

In this case, 1, 2, 4, 9, and 16 are the common factors, since 1, 2, 3, 4, 6, and 12 are the factors of 12, whereas 1, 2, 4, 8, and 16 are the factors of 16.

Is 16 a composite number?

It is true that 16 is a composite number since it has more than two components.

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