Factors Of 36 | Easy Division | Prime Factorization

Factors Of 36

In mathematics, factors of 36 are the numbers that divide 36 precisely without leaving a remainder. However, 36 can have positive or negative factors, but it cannot be decimal or fraction. 

36 can be expressed as (1, 36) or (-1, -36). The original number is the result of multiplying two negative numbers, such as -1 and -36. 

You will learn the factors of 36, the pair factors, and the prime factors of 36, along with many solved examples.

What are the Factors of 36?

36 is the product of multiplying pairs of numbers that resulted in 36. Since 36 is a composite number, it has more factors than one or the number itself. Therefore, 36 has the factors 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36

Prime Factorization of 36: 2 × 2 × 3 × 3  or 22 × 32

What are the Factors of -36?

To get the product -36, we multiply two numbers as follows:

-18 x  2 =  -36   or   18 x -2 = -3

-12 x 3 =  -36    or    12  x  -3 = -36

-9 x  4 = -36      or      9 x  -4 = -36

-6 x  6 = -36      or      6 x  -6 = -36

-36 x  1 = -36    or      36 x  -1 = -36 

Factors of -36: -1, -2, -3, -4, -6, -9, -12, -18, and -36.

Pair Factors of 36

According to the preceding discussion, the pair factors of 36 can be either positive or negative. Pair factors are multiples of two numbers that result in the original number 36. Here are the positive and negative pair factors:

Positive Pair Factors of 36:

Negative Pair Factors of 36:

Prime Factorization of 36

In order to write 36 as a product of 36 prime factors, we use prime factorization. Divide 36 by the least prime number, 2, to find the prime factors. 

Whenever it cannot be further divided by two, divide it by the next prime number, 3, until the end product is one. 

Here is a step-by-step format on how to prime factorize 36.

Divide 36 by 2

36 ÷ 2 = 18

Divide 18 by 2 once more

18 ÷ 2 = 9

In the case of 9, since 2 is no longer divisible by 9, move on to the following prime number, 3.

9 ÷ 3 = 3

To finish, divide 3 by 3 to get 1.

3 ÷ 3 = 1

By completing the above steps, we can conclude that the prime factor for 36 is 2 × 2 × 3 × 3 or  2² × 3². 

The method, as mentioned above, will also work for all large numbers, not just 36.

Examples

Example 1:

What are the common factors of 36 and 27?

Solution:

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

Prime factorization of 27 = 1, 3, 9, and 27.

Therefore, 36 and 27 have common factors of 1, 3, and 9.

Example 2:

Calculate the common factors of 36 and 37.

Solution:

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

Factors 37 are 1 and 37.

Hence, 36 and 37 have a common factor of 1 since 37 is a prime number.

Example 3:

What are the common factors of 36 and 24?

Solution:

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

Factor pairs of 24 = 1, 2, 3, 4, 6, 8, 12, and 24.

Consequently, 36 and 24 have the same common factors of 1, 2, 3, 4, 6, and 12

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