# Factors of 16

The factors of 16 are the numbers that completely divide 16 without leaving a remainder. Thus we can say that the factors of 16 are the divisors of 16. In this section, we will learn about the factors of 16 and the prime factors of 16.

#### Highlights of Factors of 16

• 16=2×2×2×2 is the prime factorization of 16.
• The factors of 16 are 1, 2, 4, 8, and 16.
• 2 is the only prime factor of 16.
• The negative factors of 16 are -1, -2, -4, -8 and -16.

#### What are the factors of 16?

If 16=a×b, then both a and b are the factors of 16. Thus to find the factors of 16, we need to write the number 16 multiplicatively in all possible ways. Note that we have:

 16 = 1×16 ∴ 1, 16 are factors of 16. 16 = 2×8 ∴ 2, 8 are factors of 16. 16 = 4×4 ∴ 4 is a factor of 16.

As there are no other ways we can express 16 multiplicatively, we will stop now, and we have obtained all the factors of 16. So the factors of 16 are 1, 2, 4, 8, and 16.

It is known that if m is a factor of 16, then -m is also a factor of 16. So the negative factors of 16 are -1, -2, -4, -8, and -16.

#### Pair Factors of 16

At first, we will find the positive pair factors of 16.

 16 = a×b Factors in Pairs (a,b) 16 = 1×16 (1, 16) 16 = 2×8 (2, 8) 16 = 4×4 (4, 4)

Thus the positive pair factors of 16 are (1, 16), (2, 8), and (4, 4). We know that if (a, b) is a positive pair factor of 16, then (-a, -b) is a negative pair factor of 16. Thus, all the negative pair factors of 16 are given below. They are:

(-1, -16), (-2, -8) and (-4, -4).

For more details of factors, visit the page: Basic concepts of factors.

Also Read: Square root of 16

#### Number of factors of 16

From above we see that the factors of 16 are 1, 2, 4, 8, and 16.

Therefore the total number of factors of 16 is five.

#### Prime Factors of 16

We have found above that the factors of 16 are 1, 2, 4, 8, and 16. Among those factors, we observe that only 2 is a prime number as it does not have any proper divisors.

∴ the only prime factor of 16 is 2.

Question: What are the factors of 16?

Video Solution:

 Factors of 8: 1, 2, 4, 8 Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 20: 1, 2, 4, 5, 10, 20 Factors of 32: 1, 2, 4, 8, 16, 32

#### How to find factors of 16?

By division method, we will determine the factors of 16. In this method, we will find the numbers that can divide 16 completely without a remainder.

 16/1=16 and the remainder is 0. ∴ 1 and 16 are factors of 16. 16/2=8 and the remainder is 0. ∴ 2 and 8 are factors of 16. 16/4=4 and the remainder is 0. ∴ 4 and 4 are factors of 16.  ⇒ 4 is a factor of 16.

Note that no numbers other than 1, 2, 4, 8, and 16 can divide 16. So the numbers 1, 2, 4, 8, and 16 are the complete list of factors of 16.