# Factors of 16

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

#### How to find factors of a number

 1.   Find factors of 16 using Division Method 2.   Find factors of 16 using Prime Factorization 3.   Find factors of 16 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 16

• Divide 16 by 1: 16 ÷ 1 : Remainder = 0
• Divide 16 by 2: 16 ÷ 2 : Remainder = 0
• Divide 16 by 4: 16 ÷ 4 : Remainder = 0
• Divide 16 by 8: 16 ÷ 8 : Remainder = 0
• Divide 16 by 16: 16 ÷ 16 : Remainder = 0

Hence, Factors of 16 are 1, 2, 4, 8, and 16

#### 2. Steps to find factors of 16 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 16 using the division method, follow these steps:

• Step 1. Start dividing 16 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 16, which is 2. Divide 16 by 2 to obtain the quotient (8).
16 ÷ 2 = 8
• Step 3. Repeat step 1 with the obtained quotient (8).
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1

So, the prime factorization of 16 is, 16 = 2 x 2 x 2 x 2.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 16 as shown below:

So, the prime factorization of 16 is, 16 = 2 x 2 x 2 x 2.

#### 3. Find factors of 16 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 16 would be the two numbers which, when multiplied, give 16 as the result.

The following table represents the calculation of factors of 16 in pairs:

Factor Pair Pair Factorization
1 and 16 1 x 16 = 16
2 and 8 2 x 8 = 16
4 and 4 4 x 4 = 16

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 16. They are called negative pair factors.

Hence, the negative pairs of 16 would be ( -1 , -16 ) , ( -2 , -8 ) and ( -4 , -4 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 16 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 16.
• Every number is a factor of zero (0), since 16 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 4, 8, 16 are exact divisors of 16.
• Factors of 16 are 1, 2, 4, 8, 16. Each factor divides 16 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16 are all less than or equal to 16.

• Which is the smallest prime factor of 16?

The smallest prime factor of 16 is 2.

• Is 16 a whole number?

Yes 16 is a whole number.

• What are the prime factors of 16?

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

• What two numbers make 16?

Two numbers that make 16 are 2 and 8.

• What are multiples of 16?

First five multiples of 16 are 32, 48, 64, 80.

• What is the sum of all factors of 16?

The sum of all factors of 16 is 31.

• What are five multiples of 16?

First five multiples of 16 are 32, 48, 64, 80, 96.

• Is 16 a perfect square?

Yes 16 is a perfect square.

• What is the greatest prime factors of 16?

The greatest prime factor of 16 is 2.

#### Examples of Factors

How many factors are there for 16?

Factors of 16 are 1, 2, 4, 8, 16.
So there are in total 5 factors.

Kevin has been asked to write 4 factor(s) of 16. Can you predict the answer?

4 factor(s) of 16 are 1, 2, 4, 8.

Sammy is puzzled while calculating the prime factors of 16. Can you help him find them?

Factors of 16 are 1, 2, 4, 8, 16.
Prime factors of 16 are 2, 2, 2, 2

What is prime factorization of 16?

Prime factorization of 16 is 2 x 2 x 2 x 2 = 24.

Ariel has been assigned the task to find the product of all the prime factors of 16. Can you help her?

Prime factors of 16 are 2, 2, 2, 2.
Hence, the product of prime factors of 2.

Can you help Rubel to find out the product of the even factors of 16?

Factors of 16 are 1, 2, 4, 8, 16.
Even factors of 16 are 2, 4, 8, 16.
Hence, product of even factors of 16 is; 2 x 4 x 8 x 16 = 1024.

Joy wants to calculate mean of all the factors of 16. Help him in finding the mean of 16.

Factors of 16 are 1, 2, 4, 8, 16.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 16 is 1 + 2 + 4 + 8 + 16 = 31.
Hence, the mean of factors of 16 is 31 ÷ 5 = 6.20.