Factors of 32

Factors of 32 are 1, 2, 4, 8, 16, 32. The factors of 32 are the numbers that can divide 32 with zero remainder. These numbers when multiplied in a defined pair give the product 32. These factors include both positive and negative integers, as well as 1 and 32.

In this article, we will discuss all the topics related to the factors of 32, including all the factors of 32, both prime factors, and methods to find these factors.

What are Factors of 32?

The factors of 32 are those numbers that can evenly divide 32 without leaving a remainder. For example, 32 can be divided by 2 with a quotient of 16. Similarly,

• 4 is the factor of 32 as 32 ÷ 4 = 8.
• 8 is a factor of 32 as 32 ÷ 8 = 4.
• 16 is a factor of 32 as 32 ÷ 16 = 2.
• 32 is a factor of 32 as 32 ÷ 32 = 1.

Hence, factors of 32 are 1, 2, 4, 8, 16 and 32.

Factors of 32 Calculator

Try out the following calculator to find the factors of 32

All Factors of 32

The factors of 32 are: 1, 2, 4, 8, 16 and 32

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How to Find the Factors of 32?

To find the factors of 32 we can use the following two methods:

• Factors of 32 using Division Method
• Factors of 32 using Multiplication Method

Factors of 32 using Division Method

To find the factors of 32 using division method, we have to divide 32 by a number and check if it completely divides 32 or not. If a number divides 32 exactly then it is a factor of 32. The quotient obtained in this division is also a factor of 32.

• 32 ÷ 1 = 32 ⇒ 1 and 32 are factors of 32
• 32 ÷ 2 = 16 ⇒ 2 and 16 are factors of 32
• 32 ÷ 3 = Not Perfect Division ⇒ 3 is not a factor of 32
• 32 ÷ 4 = 8 ⇒ 4 and 8 are factors of 32

Hence, from division method 1, 2, 4, 8, 16 and 32 are factors of 32.

Factors of 32 using Multiplication Method

Two numbers when multiplied together and yield the product 32 then the two numbers are the factors of 32. This can be shown as below:

• 1 × 32 = 32 ⇒ 1 and 32 are the factors of 32
• 2 × 16 = 32 ⇒ 2 and 16 are the factors of 32
• 4 × 8 = 32 ⇒ 4 and 8 are the factors of 32

Hence, using multiplication method we find that 1, 2, 4, 8, 16 and 32 are the factors of 32

Prime Factorization of 32

Prime Factorization of 32 is the process of showing 32 as the product of its prime factors. In this we start dividing the number 32 with the smallest possible prime number. In case of 32, the smallest possible prime number which can divide 32 is 2. Then the quotient obtained is again divided. This subsequent division goes on till we obtain 1 in the quotient. The prime factorization of 32 is shown below:

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Prime Factors of 32

The prime factorization of 32 is given as 2 × 2 × 2 × 2 × 2. Hence, the Prime factor of 32 is 2 only.

Factor Tree of 32

Factor tree is a chart that shows all the prime factors of a number in the form of a branches of a tree. for 32 we can make the factor tree of 32 as follows:

Factor Pairs of 32

Factors Pairs of 32 are the pair of numbers either both positive or both negative that when multiplied together give the product of 32. There can two types of possible factors of 32 which are mentioned below:

• Positive Factor Pairs of 32
• Negative Factor Pairs of 32

Positive Factor Pairs of 32

Positive Numbers as the factor pair are shown below:

• 1 × 32 = 32
• 2 × 16 = 32
• 4 × 8 = 32

Hence, the positive factor pairs of 32 are (1, 32), (2, 16) and (4, 8)

Negative Factor Pairs of 32

• (-1) × (-32) = 32
• (-2) × (-16) = 32
• (-4) × (-8) = 32

Hence, the positive factor pairs of 32 are (-1, -32), (-2, -16) and (-4, -8)

Solved Examples on Factors of 32

Example 1: Find the common factors of 32 and 64.

Solution:

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

Factors of 64 = 1, 2, 4, 8, 16, 32 and 64

Common factors = 1, 2, 4, 8, 16 and 32.

Example 2: Is 32 a prime number?

Solution:

The factors of 32 are = 1, 2, 4, 8, 16 and 32

Since 32 has more than two factors, it is not a prime number.

Example 4: Find the sum of the factors of 32?

Solution:

The factors of 32 are = 1, 2, 4, 8, 16 and 32

The sum therefore is, 1 + 2 + 4 + 8 + 16 + 32 = 63

Factors of 32 Practice Problems

Q1: What is the greatest prime factor of 32?

Q2: What will be the value of a, if a × b = 32 and b = 16?

Q3: What is the difference between the greatest and smallest factors of the number 32?

Q4: Find the common factors of 32 and 96.

Q5: Are there any common numbers in the factors and multiples of 32?

Factors of 32 Frequently Asked Questions

What are Factors of 32?

The factors of 32 are 1, 2, 4, 8, 16 and 32

How do you Find the Factors of 32?

We can find the factors of 32 using multiplication and divison method.

What is the Prime Factorization of 32?

The prime factorization of 32 is 2 × 2 × 2 × 2 × 2.

What is Greatest Common Factor (GCF) of 32 and 64?

The GCF of 32 and 64 is 32.

Is 2⁵ equivalent to the Prime Factorization of 32?

Yes, because the prime factorization of 32 is 2 × 2 × 2 x 2 x 2.

What is the Sum of All the Factors of 32?

The sum of all the factors of 32 is 63.

Which is the Largest Factor of 32?

32 itself is the largest factor of 32.