# Factors of 32

Factors of 32 are 1, 2, 4, 8, 16, and 32

#### How to find factors of a number

 1.   Find factors of 32 using Division Method 2.   Find factors of 32 using Prime Factorization 3.   Find factors of 32 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 32

• Divide 32 by 1: 32 ÷ 1 : Remainder = 0
• Divide 32 by 2: 32 ÷ 2 : Remainder = 0
• Divide 32 by 4: 32 ÷ 4 : Remainder = 0
• Divide 32 by 8: 32 ÷ 8 : Remainder = 0
• Divide 32 by 16: 32 ÷ 16 : Remainder = 0
• Divide 32 by 32: 32 ÷ 32 : Remainder = 0

Hence, Factors of 32 are 1, 2, 4, 8, 16, and 32

#### 2. Steps to find factors of 32 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 32 using the division method, follow these steps:

• Step 1. Start dividing 32 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 32, which is 2. Divide 32 by 2 to obtain the quotient (16).
32 ÷ 2 = 16
• Step 3. Repeat step 1 with the obtained quotient (16).
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1

So, the prime factorization of 32 is, 32 = 2 x 2 x 2 x 2 x 2.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 32 as shown below:

So, the prime factorization of 32 is, 32 = 2 x 2 x 2 x 2 x 2.

#### 3. Find factors of 32 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 32 would be the two numbers which, when multiplied, give 32 as the result.

The following table represents the calculation of factors of 32 in pairs:

Factor Pair Pair Factorization
1 and 32 1 x 32 = 32
2 and 16 2 x 16 = 32
4 and 8 4 x 8 = 32

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 32. They are called negative pair factors.

Hence, the negative pairs of 32 would be ( -1 , -32 ) , ( -2 , -16 ) and ( -4 , -8 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 32 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 32.
• Every number is a factor of zero (0), since 32 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, 32 are exact divisors of 32.
• Factors of 32 are 1, 2, 4, 8, 16, 32. Each factor divides 32 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16, 32 are all less than or equal to 32.

• What are the pair factors of 32?

Pair factors of 32 are (1,32), (2,16), (4,8).

• What are five multiples of 32?

First five multiples of 32 are 64, 96, 128, 160, 192.

• What two numbers make 32?

Two numbers that make 32 are 2 and 16.

• What is the sum of all factors of 32?

The sum of all factors of 32 is 63.

• What are factors of -32?

Factors of -32 are -1, -2, -4, -8, -16, -32.

• What are factors of 32?

Factors of 32 are 1, 2, 4, 8, 16, 32.

• Is 32 a perfect square?

No 32 is not a perfect square.

• Which is the smallest prime factor of 32?

Smallest prime factor of 32 is 2.

• Which is greatest factor of 32?

The greatest factor of 32 is 16.

#### Examples of Factors

Can you help Sammy find out the product of the odd factors of 32?

Factors of 32 are 1, 2, 4, 8, 16, 32.
Odd factors of 32 are 1.
Hence product of odd factors of 32 is; 1 = 1.

Joey wants to write all the prime factors of 32 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 32 are 2, 2, 2, 2, 2.
So in exponential form it can be written as 25.

How many factors are there for 32?

Factors of 32 are 1, 2, 4, 8, 16, 32.
So there are in total 6 factors.

Kevin has been asked to write 5 factor(s) of 32. Can you predict the answer?

5 factor(s) of 32 are 1, 2, 4, 8, 16.

Sammy is puzzled while calculating the prime factors of 32. Can you help him find them?

Factors of 32 are 1, 2, 4, 8, 16, 32.
Prime factors of 32 are 2, 2, 2, 2, 2

What is prime factorization of 32?

Prime factorization of 32 is 2 x 2 x 2 x 2 x 2 = 25.

Can you help Rubel to find out the product of the even factors of 32?

Factors of 32 are 1, 2, 4, 8, 16, 32.
Even factors of 32 are 2, 4, 8, 16, 32.
Hence, product of even factors of 32 is; 2 x 4 x 8 x 16 x 32 = 32768.