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Factors

Factors of 32 | Prime Factorization of 32 | Factor Tree of 32

Written by Prerit Jain

Updated on: 18 Aug 2023

Contents

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Factors of 32 | Prime Factorization of 32 | Factor Tree of 32

Factors of 32 | Prime Factorization of 32 | Factor Tree of 32

Factors of 32: There are a total of 7 factors for the number 32. The list of numbers that divide the given number completely is known as its factors. In the case of 32, the numbers 1, 2, 4, 8, 16, 32, and 64 will divide the number 32 evenly. Hence, the factors of 32 are 1, 2, 4, 8, 16, 32, and 64.

The factors of a number can be both positive and negative and are also written in the pair format. This means that multiplying the set of two factors in pairs gives the original product (32). In this article, let us discuss how to find factors of 32, its prime factorization, and factor trees with solved examples. Keep reading to learn more.

What Are the Factors of 32?

The factors of 32 are the numbers that divide the number (32) evenly without leaving any remainder. The factors of a number can be both positive and negative. Hence, the number 32 has both positive and negative factors.

Factors of 32: 1, 2, 4, 8, 16, 32 and 64
Negative Factors of 32: -1, -2, -4, -8, -16, -32 and -64
Prime Factorization of 32: 2 X 2 X 2 X 2 X 2 or 25
Pair Factors of 32: 25
Prime Factors of 32: 25
Sum of Factors of 32: 127
Sum of Prime Factors of 32: 3
Factors of 32

 

What Are the Factors of 32 in Pairs?

A pair factor of 32 is a combination of two numbers, which when multiplied together gives the product of the original number (32). These pair factors are also written in positive and negative pairs as shown in the table below:

Positive Factor Pairs of 32

The positive pair factors of 32 are (1, 32), (2, 16), and (4, 8).

Positive Pair Factors of 32

 

Negative Factors Pairs of 32

The negative pair factors of 32 are (-1, -32), (-2, -16) and (-4, -8).

Negative Pair Factors of 32

How To Find Factors of 32 Through Division Method?

To determine the factors of 32, we are using the division method. This approach requires you to multiply a sequence of natural integers by 32. The numbers that divide the 32 completely without leaving any remainder are known as factors of 32. The following are the detailed steps for finding the factors of 32 using the division method:

  • 32 ÷ 1 = 32
  • 32 ÷ 2 = 16
  • 32 ÷ 4 = 8
  • 32 ÷ 8 = 4
  • 32 ÷ 16 = 2
  • 32 ÷ 32 = 1
  • 64 ÷ 2= 32

Therefore, we can see that 1, 2, 4, 8, 16, and 32 are the numbers that do not leave any remainder when divided by 32. Hence, the factors of 32 are 1, 2, 4, 8, 16, and 32. 64 is also a factor of 32, though it cannot divide by 32. But 32 can divide it by 2.

What Is the Prime Factorization of 32?

Check if the given number is a prime number. If the given number is a prime number then there will be only two factors i.e 1 and the number itself. If the given number is a composite number, then it will have more than two factors.
Since 32 has more than two factors, it’s a composite number. Hence, we can use the prime factorization method to find the factors of 32.


The steps to find prime factors of 32 using the prime factorization method are given below:

Step 1: Divide the number 32 by the smallest prime number that is divisible by 32. Hence the smallest prime number that is divisible by 32 is 2. So, 32 ÷ 2 = 16

Step 2: Now, divide the number 16 (quotient) by the smallest prime number which is 2. So, 16 ÷ 2 = 8

Step 3: Divide the quotient by 2 repeatedly until you get the number prime number as the quotient. 8 ÷ 2 = 4, 4 ÷ 2 = 2

Step 4: Now we got 2 as the quotient. Dividing 2 with 2 gives us 1. So, 2 ÷ 2 = 1 The quotient is 1. Since 1 cannot be divided further, the prime factors of 32 are 2 X 2 X 2 X 2 X 2 or 25.

Image representation of the prime factorization of 32:

Prime Factorization of 32

What Is the Factor Tree of 32?

Students can also use the factor tree to find the prime factors of 32. In this method, we will place the number 32 at the top of the factor tree. Now, as part of the branches, we will write down any set of pair factors of the given number (32). Now, again, we will split the pair of factors into factors. This process will be continued until the branches become prime numbers. Now, circling all the prime numbers will give us the prime factors of 32.

Step 1: Let’s place the number 32 at the top of the factor tree and write down 32 in pairs, that is, 2 and 16.

Step 2: Since 2 is a prime number, we can no longer separate it. Let us circle 2 and move on to the next number. We will now divide 16 into 2 and 8.

Step 3: As we can see, 2 is a prime number but 8 is not, so we will split 8 into 2 and 4.

Step 4: Now again, we will leave 2 as it is because it is a prime number, but we will break 4 into 2 and 2.

Step 5: We can see that 2 is a prime number. The branches in the factor tree will now be all the prime numbers. Hence, circling all the branches, 25 or 2 X 2 X 2 X 2 X 2= 32, which are 32 prime factors.

There are many ways in which we can write the factor tree of 32. Below is an image representation of the factor tree of 32, choosing 4 and 8 as pair factors of 32.

Factor tree of 32

Factors of 32 Pattern

The pattern that we observe from the factors of 32 is explained below:
Factors of 32 = 1, 2, 4, 8, 16, 32 and 64
From the above, it is clear that the numbers are doubling.
1, 2, 4, 8, 16, 32, 64
Also, the pattern of 32 prime factorizations is as follows:

2,
2, 2,
2, 2, 2,
2, 2, 2, 2
2, 2, 2, 2, 2

Solved Examples on Factors of 32

Here are some solved examples of 32 factors:

What is the sum of all the factors of 32?
1, 2, 4, 8, 16, 32, and 64 are the 32 factors.
1 + 2 + 4 + 8+ 16 + 32 + 64 = 127
Hence, 127 is the sum of all 32 factors.

What are the factors and prime factors of 32?
The factors of 32 are 1, 2, 4, 8, 16, 32, and 64.
The prime factors 32 are: 25 or 2 X 2 X 2 X 2 X 2.

What’s the highest common factor between 48 and 32?
Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
Factors of 32 are 1, 2, 4, 8, 16, 32, and 64.
Hence, the common factors of 48 and 32 are 1, 2, 4, 8, and 16.
So, the highest common factor between 48 and 32 is 16.

What’s the highest common factor between 56 and 32?
Factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
Factors of 32 are 1, 2, 4, 8, 16, 32, and 64.
Hence, the common factors of 56 and 32 are 1, 2, 4, and 8.
So, the highest common factor between 56 and 32 is 8.

Is 16 a factor of 32?
Yes, 16 is a factor of 32.
32 ÷ 2 = 16.

What are the factors of -32?
The factors of -32 are -1, -2, -4, -8, -16, -32, and -64.

What are the common factors of 48 and 32?
To find the common factors of 80 and 32, we need to find the factors of both 48 and 32.
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.
Factors of 32: 1, 2, 4, 8, 16, 32, and 64.
Hence the common factors of 80 and 32 are 1, 2, 4, 8, and 16.

What are all the factors of 32?
The factors of 32 are 1, 2, 4, 8, 16, 32, and 64.

What are the factors of 32 that are composite?
Any number which has more than 2 factors is known as a composite number. The list of numbers that have more than 2 factors in factors of 32 are 4, 8, 16, 32, and 64.
Hence, the factors of 48 that are composite numbers are 4, 8, 16, 32, and 64.

What factors of 32 are multiples of 2?
The factors of 32 that are multiples of 2 are 2, 4, 8, 16, 32, and 64.
2 x 1 = 2
2 x 2 = 4
2 x 4 = 8
2 x 8 = 16
2 x 16 = 32
2 x 32 = 64.

How many 32 factors are odd?
There is only one odd number among the factors of 31. It is 1.

What are the factors of 32 and 48?
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
The factors of 32 are 1, 2, 4, 8, 16, 32, and 64.

How many different factors are there for the number 32?
A total of 7 factors are there for the number 32 and they are 1, 2, 4, 8, 16, 32, and 64.

How many pair factors are there in 32?
A total of 3 pairs are there in factors of 32. They are (1, 32), (2, 16), (4, 8).

What is the largest factor of 32?
The largest factor of 32 is 64.
The second largest factor of 32 is 32.

FAQs on Factors of 32

List all the factors of 32
1, 2, 4, 8, 16, 32, and 64 are the factors of 32.

What are the composite factors of 32?
4, 8, 16, 32, and 64 are the composite factors of 32. Composite factors are those that have more than 2 factors other than 1 and itself.

What are the factors of 32 in pairs?
(1, 32), (2, 16) and (4, 8) are the 32 factors of pairs.

What are the positive factors for 32?
1, 2, 4, 8, 16, 32, and 64 are the positive factors for 32.

What are some multiples of 32?
A multiple is that which can be divided by another number without a remainder.
Some multiples of 32 are 32, 64, 96, 128, 160, 192, 224, 256, 288 and 320.

Now you have all the necessary information regarding the factors of 32.

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Prerit Jain

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