FACTORS OF 16 WITH EXAMPLES AND FAQ

FACTORS OF 16

Any number is a factor of a number if it divides the number without leaving any remainder behind. For example, 2 is a factor of 4, 5 is a factor of 20, etc.16 is a composite number and hence it has factors that are other than 1 and itself. If any number divides 16 completely, i.e, without leaving any remainder, then that number is a factor of 16. 

1, 2, 4, 8 and 16 are 16’s factors. Here, 1 is the smallest factor and 16 itself is its biggest factor.

How to determine factors of 16?

Let’s find the factors by simply dividing 16 by all the numbers starting from 1 to 16 and see which number divides 16 without leaving a remainder. We see that when 16 is divided by 1, 2, 4, 8, and 16 the remainder is 0. Hence 1, 2, 4, 8, and 16 are the factors of 16.

Prime Factorization of 16

We divide 16 by prime numbers in this method. In this method, we will continue division with the quotient if it’s a composite number till the last quotient is 1. The prime factors can be obtained by (a) Division Method or (b) Factor Tree Method.

(a) Prime Factorization by Division Method

We divide the number 16 by the smallest prime number which doesn’t leave a remainder. The quotient obtained is divided repeatedly by the smallest prime number until the last quotient obtained is 1.

Divide 16 by the prime number 2 

16 ÷ 2 = 8, and continue similarly

8 ÷ 2 = 4

4 ÷ 2 = 2

2 ÷ 2 = 1

Hence the prime factorization of 16 is 2 × 2 × 2 × 2.

(b) Prime Factorization by the Factor Tree Method

We need to find the prime factorization of 16, hence, the root of the factor tree is 16. We can write the pair of factors as the branch of 16. The factor tree ends at a prime factor. 

Factor tree of 16

The factor tree ends at 2 since it is a prime number.

∴ Prime factorization of 16 is 2 × 2 × 2 × 2.

Factors of 16 in Pairs

A factor pair includes the set of two numbers whose product will give the number as the product. Factor pairs of 16 are:

1 × 16 = 16, Hence the factor pair is (1, 16).

2 × 8 = 16, Hence the factor pair is (2,8).

4 × 4 = 16, Hence the factor pair is (4, 4).

The product of two negative numbers is positive. 16’s negative factor pairs are:

(-1) × (-16) = 16, Hence the factor pair is (-1, -16).

(-2) × (-8) = 16, Hence the factor pair is (-2,-8).

(-4) × (-4) = 16, Hence the factor pair is (-4, -4).

Examples

Example 1: Do 18 and 16 have any factors in common?

Solution: There are six factors of 18 which are:

18 ÷ 1 = 18

18 ÷ 2 = 9

18 ÷ 3 = 6

18 ÷ 6 = 3

18 ÷ 9 = 2

18 ÷ 18 = 1

Hence the factors of 18 are 1, 2, 3, 6, 9, and 18 and that of 16 are 1, 2, 4, 8, and 16. Therefore, 18 and 16 have 1 and 2 as common factors.

Example 2: Find the sum of all the factors of 16.

Solution:

1, 2, 4, 8 and 16 are 16’s factors.

∴ The sum of all the factors is = 1 + 2 + 4 + 8 + 16 = 31