What are the prime factors of 32?

Factors of 32 are numbers that can divide the number 32 completely. We can find factors of 32 by performing prime factorisation. Prime factorisation or integer factorisation of a number is breaking a number down into the set of prime numbers whose product results in the original number.

Table of Contents Show

Factors of 32
Prime Factorization of 32
Common Factors of 32
Factor Pairs of 32
Steps to Find Factors of 32
Factors By Multiplication
Factors By Division
Solved Example on Factors of 32
Factors of 32 FAQs

In this article, we will learn about the factors of 32, how to find them by prime factorisation, common factors of 32 and factor pairs. We will also learn about the steps to find the factors of 32 with its factor tree of 32 and solved examples.

Factors of 32

A factor is an integer number that divides a given integer completely, leaving no remainder. A composite number will have many factors. On the other hand, a prime number has only two factors; one and the number itself.

We can find whether a number is prime or composite by checking for its divisibility test. The number 32 is divisible by 2 as it is an even number. Thus, we can conclude that the number 32 is composite and has many factors.

Now, let’s find the factors of the number 32. Number 32 is divisible by 1, 2, 4, 8, 16 and 32. Hence, the numbers 1, 2, 4, 8, 16 and 32 are factors of the number 32.

Know more about Addition and Subtraction of Polynomials here.

Prime Factorization of 32

To perform the prime factorization of 32, we start to divide it by the smallest prime number which can completely divide 32. We know that it’s 2.

\(32 = 2\times16\)

\(32 = 2\times2\times8\)

\(32 = 2\times2\times 2\times4\)

\(32 = 2\times2\times2\times2\times2\)

Thus, \(32 = 2^5\)

We can also do this by upside-down method. So, now the prime factorization of 32 with the upside-down division method is 2 × 2 × 2 × 2 × 2.

Common Factors of 32

Two or more numbers can have the same factors and they are referred to as common factors. We have seen that the factors of 32 are 1, 2, 4, 8, 16, and 32. If any of these factors are common for any other number then it becomes the common factor of the two numbers.

Example:

Factors of Number 32: 1, 2, 4, 8, 16 and 32.

Factors of Number 48: 1, 2, 3, 4, 6, 8, 12, 24, and 48.

Thus, 1, 2, 4 and 8 become the common factors.

However, the number 2 is the lowest common factor.

Learn more about Odd Numbers here.

Factor Pairs of 32

Factors always come in pairs. If one number divides a number then the quotient obtained will also divide the number. These divisors and quotients are called factor pairs. To find the factors of 32 in pairs, there is a simple method; let us try to understand the same.

Product Form of 32	Factors in Pairs
\(1\times32 = 32\)	\((1, 32)\)
\(2\times16 = 32\)	\((2, 16)\)
\(4\times8 = 32\)	\((4, 8)\)

Now let’s see the factor tree of 32.

Steps to Find Factors of 32

Multiplication and division are the two ways of determining factors of 32. Furthermore, divisibility rules can be applied in both cases.

Factors By Multiplication

To find the factors using the multiplication follow the steps below:

Step 1: Write the 32 as the product of two numbers in as many ways as possible. This will require a thorough knowledge of tables.

Step 2: The factors of 32 are all the numbers involved in these products.

Factors By Division

To find the factors using division follow the steps below:

Step 1: Find all the numbers that are smaller or equal to 32. Start from the smallest prime numbers

Step 2: Select out the numbers which can divide the given number using divisibility rules.

Step 3: Divide the given number by each of these numbers.

Step 4: The factors of the number are the divisors that give 0 as the remainder.

Learn more about the General Equation of a Line here.

Solved Example on Factors of 32

Now let’s see some solved examples on factors of 32.

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

Solution:

The factors of 32 are 1, 2, 4, 8, 16, 32 and of 64 are 1, 2, 4, 8, 16, 32, 64.

Thus, the common factors are 1, 2, 4, 8, 16, 32.

Solved Example 2: Find the factors of 32 and state why the factors of 32 will be the common factors of all multiples of 32.

Solution:

A factor of a number is a number that when multiplied by another factor of the same results in the given number.

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

Since all the multiples of 32 will contain 32, the factors of 32 will be the common factors for all its multiples.

Solved Example 3: How Many Factors of 32 are also Factors of 20?

Solution:

The factors of 32 are 1, 2, 4, 8, 16, 32 and of 20 are 1, 2, 4, 5, 10, and 20. Thus, the common factors are 1, 2, and 4.

Hope this article on the Factors of 32 was informative. Get some practice of the same on our free Testbook App. Download Now!

Factors of 32 FAQs

Ans.1 The factor pair of 32 are \((1, 32)\), \((2, 16)\), and \((4, 8)\).

Ans.2 To perform the prime factorization of 32, we start to divide it by the smallest prime number which can completely divide 32. We know that it’s 2. \(32 = 2\times16\), \(32 = 2\times2\times8\), \(32 = 2\times2\times 2\times4\) and \(32 = 2\times2\times2\times2\times2\). Thus, \(32 = 2^5\)

Ans.3 The factors of 32 are 1, 2, 4, 8, 16, and 32. Thus, 16 is the largest factor of 32 after 32 itself.

Ans.4 The factors of 32 are 1, 2, 4, 8, 16, and 32. Thus, 2 is the smallest factor of 32 after 1.

Ans.5 A factor is a number that divides a given integer by itself, leaving no residue. A composite number will have many factors. On the other hand, a prime number has only two factors, one and the number itself. Multiples of 32 are numbers that have 32 as factors.

32 is a composite number. 32 = 1 x 32, 2 x 16, or 4 x 8. Factors of 32: 1, 2, 4, 8, 16, 32. Prime factorization: 32 = 2 x 2 x 2 x 2 x 2, which can also be written 32 = 2⁵.

When 32 is a clue in the FIND THE FACTORS puzzles, always use 4 and 8 as the factors.

Here is a hook-shaped FIND THE FACTORS 1-10 puzzle, and YOU can solve in by hook or by crook!

The puzzle has a few square numbers: 16, 4, 81, 36, 36, 9, 1, and 25. Several square numbers can only be factored one way in a FIND THE FACTORS puzzle, while others can be factored 2 or 3 ways.

Obviously, 6 x 6 = 36 will not let us off the hook both times that 36 appears. One of those times we must use 4 x 9 = 36. This puzzle reminds us that 36 is sometimes a square and sometimes a rectangle.

The 16 isn’t a square in this puzzle either. Sometimes 4 and 9 are rectangles, but not in this case.

81 and 25 are always square in the FIND THE FACTORS puzzles because even though 1 and 3 are allowed to be factors, 25, 27, and 81 are greater than 10 and not allowed as possible factors to solve the puzzle.

To solve this puzzle, write the numbers from 1 to 10 in the top row and again in the first column so that those numbers are the factors of the given clues. Don’t fall for those slightly tricky clues hook, line, and sinker!

This week’s puzzles are also available in an excel file here. If you have a spreadsheet program on your computer, you can access it. If you enable editing in excel, you can type your answers directly onto the puzzle, and you can also easily print the puzzles. I’m hooked on factoring. I hope you’ll get hooked, too!

Here are all the factors to last week’s level 2 FIND THE FACTORS 1-12 snowflake puzzle: