 # Factors of 16

## Introduction To Factors of 16

16 is a composite number and all its factors are integers that can be divided evenly into 16. Also, if we divide 16 by one of its factors, we will get another factor of 16.

For example, 16 ÷ 2 = 8. Here, 2 is a factor of 16 and if we divide 16 by 2, we get 8 which is also a factor of 16 (8 x 2 = 16). Now, before jumping into the obvious question that is “What are the factors of 16?” Do we know what factors are? Let us brush up a little. Any number can be a factor of a number if it divides the number without leaving any remainder behind.

### How Can We Find The Factors Of 16?

Finding the factor of 16 is easier than counting the number of people in a room or maybe the alphabet in English Language. To find the factor of 16 we just need to divide 16 by all the numbers starting from 1 to 16 and see which number divides 16 without leaving a remainder. What are we waiting for? Let us do it and find out all the factors of 16.

16 ÷ 1 = 16

16 ÷ 2 = 8

16 ÷ 3 = 5.3

16 ÷ 4 = 4

16 ÷ 5 = 3.2

16 ÷ 6 = 2.6

16 ÷ 7 = 2.28

16 ÷ 8 = 2

16 ÷ 9 = 1.7

16 ÷ 10 = 1.6

16 ÷ 11 = 1.4

16 ÷ 12 = 1.3

16 ÷ 13 = 1.2

16 ÷ 14 = 1.1

16 ÷ 15 = 1.0

16 ÷ 16 = 1

Therefore, we can clearly see that number 1, 2, 4, 8 and 16 are the only factors of 16. Rest of the numbers leave a remainder as they result in decimal numbers and cannot be the factors of 16.

### How Many Factors Of 16 Are There?

From the above finding we can calculate that there are 5 factors of 16 including 1 and these factors are: 1, 2, 4, 8, and 16. All the factors of 16 are composite except 1 and 2. 2 is the only prime factor among all the other factors of 16 and according to the definition, 1 is neither a prime number nor a composite number. These are the integers that divide 16 evenly without any remainder. We can express these integers either individually or as a paired factor.

### Pair Factors Of 16

Pair factors are combinations of any two factors which when multiplied together gives 16 as the product. Here we can see all the Positive pair factors of 16.

1 × 16 = 16     therefore, we can say that 1 and 16 are the pair factors of 16.

2 × 8 = 16       therefore, we can say that 2 and 8 are the pair factors of 16.

4 × 4 = 16       therefore, we can say that 4 and 4 are the pair factors of 16.

8 × 2 = 16       therefore, we can say that 8 and 2 are the pair factors of 16.

16 × 1 = 16     therefore, we can say that 16 and 1 are the pair factors of 16.

Prime Factorization

We can factor a set of numbers where each number is a prime number, and the method to do that is called prime factorization. The prime factorization of 16 can be written as 2 x 2 x 2 x 2.

16 is a composite number and thus unlike prime numbers, 16 has more than two factorizations.

To prove the statement select the rightmost and leftmost integers in 16, 8, 4, 2, 1 and then multiply these integers to get 16. This will be the first factorization. Secondly, we have to choose the second rightmost and the second leftmost integer to get the 2nd factorization which also results in 16.

The prime factorization also called integer factorization of 16 can be defined as determining a set of prime numbers which if multiplied together, will result in the original number 16. We can also call it prime decomposition of 16.

The factors of 16 are 1, 2, 4, 8, 16, now if we find the prime factorization of 16, the result would be 16 = 2 x 2 x 2 x 2, which can also be written as 16 = 2⁴.  Since √16 = 4, which is a whole number, it can also be called as a perfect square.

### Factor Tree Of 16

Why do we call it a factor tree? Well, that is because just like a tree has branches, a factor tree has sub-factors which can be graphically represented. This is the man-made tree of numbers which grows when we find the factors of a number and then find the factors of the factors of the number. The process continues until we reach a stage where we have a bunch of prime factors which will also be the prime factorization of the original number.  Here, we will make it easy for you to understand:

### Solved Examples

Example 1) Find the factors of the following:

i) 124

ii) 72

iii) 66

iv) 57

v) 180

vi) 52

vii) 86

viii) 120

ix) 92

x) 196

Answer 1) Finding the factors of the following numbers:

i) The factors of 124 are:

 2 124 2 62 31 31 1

ii) Factors of 72 are:

 2 72 2 36 2 18 3 9 3 3 1

iii) Factors of 66 are:

 3 66 2 22 11 11 1

iv) Factors of 57 are:

 3 57 19 19 1

v) Factors of 180 are:

 2 180 2 90 5 45 7 7 1

vi) Factors of 52 are:

 2 52 2 26 13 13 1

vii) Factors of 86 are:

 2 86 43 43 1

viii) Factors of 120 are:

 2 120 2 60 2 30 3 15 5 5 1

ix) Factors of 92 are:

 2 92 2 46 23 23 1

x) Factors of 196 are:

 2 196 2 98 7 49 7 7 1