Factors Of 36 – With Division and Prime Factorization

factors of 36

Factors Of 36

In mathematics, factors of 36 are the numbers that divide 36 exactly 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 result of multiplying two negative numbers, such as -1 and -36, is the original number. 

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

factors of 36

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 multiplies of two numbers that result in the original number 36. Here are the positive and negative pair factors:

Positive Pair Factors of 36:

Positive Factors of 36Positive Pair Factors of 36
1 × 36 (1, 36)
2 × 18 (2, 18)
3 × 12(3, 12)
4 × 9(4, 9)
6 × 6(6, 6)

Negative Pair Factors of 36:

Negative Factors of 36Negative Pair Factors of 36
-1 × -36 (-1, -36)
-2 × -18 (-2, -18)
-3 × -12(-3, -12)
-4 × -9(-4, -9)
-6 × -6(-6, -6)

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 with 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.

factors of 36 by prime factorization

Examples

Example 1:

What are the common factors of 36 and 35?

Solution:

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

35 has the factors 1, 5, 7, and 35.

Therefore, 36 and 35 have a common factor of 1.

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.

The factors of 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 72?

Solution:

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

Factors of 72 = 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and 72.

Consequently, 36 and 72 have the same common factors of 1, 2, 3, 4, 6, 9, 12, 18, and 36.

FAQs

How many factors are there in 36?

Numbers that divide 36 precisely without leaving any remainder are the factors of 36. As a result, 36 has factors 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Using 36 as the prime factorization, what is its prime factorization?

Prime factorization of 36 is 2 × 2 × 3 × 3 or 22 × 32.

How many positive pair factors does 36 have?

For 36, the positive pair factors are (1, 36), (2, 18), (3, 12), (4, 9) and (6, 6).

What are the negative pair factors of 36?

(-1, -36), (-2, -18), (-3, -12), (-4, -9), and (-6, -6)  are the negative pair factors of 36.

9 is a factor of 36; is it true?

9 is indeed a factor of 36. 

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