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 divide 36 without leaving a remainder.

In this article, we will learn about “What are Factors?”, “What are 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.

What are Factors of 36?

The factors of 36 are the numbers that can be multiplied together to result in 36 itself. For Example,

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

List of all 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.

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 of 36?

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

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

These pairs represent all the factor pairs of 36: (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6). Factors pairs of a number can be positive as well as negative.

Positive Pairs of Factors of 36

Below is the list of positive factor pairs of 36:

Pairs	Factors
1	1, 36
2	2, 18
3	3, 12
4	4, 9
5	6, 6

Negative Pairs of Factors of 36

Below is the list of negative factor pairs of 36:

Pairs	Factors
1	-1, -36
2	-2, -18
3	-3, -12
4	-4, -9
5	-6, -6

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:

Factor Tree of 36

Read More,

• Factors of 12
• Factors of 9
• Factors of 72

Prime Factors of 36 – FAQs

What are Factors of 36?

The factors of Thirty-Six 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

What is a Factor?

In mathematics, a factor is a number or algebraic expression that divides another number or expression evenly, without a remainder. For example, 5 and 2 are factors of 10 because 5 × 2 = 10.

How Many Factors does 36 have?

The number 36 has a total of 9 factors: 1, 2, 3, 4, 6, 9, 12, 18, and 36.

What is Factor Tree of 36?

36

↙ ↘

2 18

↙ ↘

2 9

↙ ↘

3 3

Write 36 as a Product of Prime Factors.

36 = 2×2×3×3 = 2²×3²

Is 12 a factor of 36?

Yes, 12 is a factor of 36, as 12×3 = 36

What are Multiples of 36?

Multiples of 36 are 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, 396, 432, 468, 504, 540, 576, 612, 648, 684, 720, and so on.