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 divide 36 without leaving a remainder.

Let’s learn how to find the factors of 36 using the prime factorization method.

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 factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Positive Pairs of Factors 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:

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

Prime Factors of 36

• Prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.
• Factor of a number is a natural number that divides evenly into that number.
• Prime factorization of a number is the expression of that number as a product of its prime factors.
• In the next steps, we will see how to calculate the prime factorization of 36.

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

Read More about Prime Factorization

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).

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

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.