Factors of 36

Factors of thirty-six are 1, 2, 3, 4, 6, 9, 12, 18, and 36. These numbers are all divisors of 36, which means they can divide 36 without leaving a remainder. Factors are the building blocks of numbers, and finding them helps us break down a number into its smaller components.

In this article, we will learn about “What are Factors?”, “Factors of 36?”, and “How to Find Factors of 36?”.

What are Factors?

Factors of a number are the whole numbers that can be multiplied together to produce that number. For example, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Factors can be categorized into two types:

• Prime Factors: These are factors that are prime numbers. Prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves. For example, the prime factors of 36 are 2 and 3.
• Composite Factors: These are factors that are composite numbers, meaning they have more than two factors. For example, 4, 6, 9, 12 and 18 are composite factors of 36.

Factors of 36

The factors of 36 are the numbers that divide 36 exactly without leaving any remainder. Thus, the list of factors of 36 are 1, 2, 3, 4, 6, 9, 18, and 36.

• 1 × 36 = 36
• 2 × 18 = 36
• 3 × 12 = 36
• 4 × 9 = 36
• 6 × 6 = 36

Prime Factors of 36

To find the prime factors of 36, you can start by dividing it by the smallest prime number, which is 2, and then continue dividing by prime numbers until you can not divide anymore.

1. Divide 36 by 2: 36÷2 = 18
2. Divide 18 by 2: 18÷2 = 9
3. Divide 9 by 3: 9÷3 = 3

Now, since 3 is also a prime number, we stop here because we can not divide 3 further.

So, the prime factors of 36 are 2 × 2 × 3 × 3, or simply 2² × 3².

How to Find Factors?

To find the factors of a number, we have to identify all the numbers that can be multiplied together to give that number.

Follow the given steps to find factors of a number:

Step 1. Start with 1 and the Number Itself:

• Every number has at least two factors: 1 and the number itself.

Step 2.Divide the Number by Integers:

• Start dividing the number by integers starting from 1 up to the square root of the number.
• If the division results in a whole number (no remainder), both the divisor and the quotient are factors.

Step 3.List the Factors:

• Write down all the factors obtained in the step 2.

For 36:

1 × 36 = 36

2 × 18 = 36

3 × 12 = 36

4 × 9 = 36

6 × 6 = 36

These pairs give us all the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Prime Factorization of 36

To perform Prime Factorization of 36, we have to find all the factors of 36, then we need to identify the prime numbers among them.

Step 1: Find all factors of 36:

• 1×36 = 36
• 2×18 = 36
• 3×12 = 36
• 4×9 = 36
• 6×6 = 36

Step 2: Identify prime numbers among factors:

Among all the factors of 36, only 2 and 3 are prime.

Step 3: Now, we can write prime factorization of 36 as:

36 = 2² × 3²

Factor Pairs of 36

The factor pairs of 36 are the pairs of numbers that can be multiplied together to give 36. Here they are:

1 × 36 = 36

2 × 18 = 36

3 × 12 = 36

4 × 9 = 36

6 × 6 = 36

Factor Tree of 36

A factor tree, also known as a number tree, is a visual diagram used to display the factors of a number. It breaks down a number into its simplest factors.

• A factor tree starts with the number at the top of the tree. It then lists the various factors as "branches".
• Each branch in the tree is split into factors. Once the factor at the end of the branch is a prime number, the branch stops.
• The ends of the factor tree are all the prime factors of the original number.

Factor Tree of 36 is shown in the below diagram:

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