The number 36 can be factored into several pairs of integers. The factors of 36 are the numbers that can be multiplied together to give the product 36. Here are the factor pairs for 36:

1 and 36

2 and 18

3 and 12

4 and 9

6 and 6

These are all the possible combinations of two numbers that multiply to give 36. In addition to these factor pairs, 36 is also divisible by other numbers such as itself (36) and 1.

## Factors of 36 definition

The factors of 36 are the numbers that divide evenly into 36 without leaving a remainder. In other words, factors are the integers that can be multiplied together to obtain the number 36. For example, 1, 2, 3, 4, 6, 9, 12, 18, and 36 are all factors of 36 because they divide evenly into 36.

To find the factors of 36, you can follow these steps:

- Start with the number 1, as it is always a factor of any number.
- Divide 36 by 2. If the division yields an integer result (no remainder), then 2 is a factor of 36. In this case, it is.
- Continue dividing 36 by consecutive integers (3, 4, 5, …) up to the square root of 36, which is approximately 6.

- Divide 36 by 3. It results in 12, which is an integer, so 3 is a factor of 36.
- Divide 36 by 4. It results in 9, which is an integer, so 4 is a factor of 36.
- Divide 36 by 5. The result is not an integer.
- Divide 36 by 6. It results in 6, which is an integer, so 6 is a factor of 36.

- By this point, you have covered all the possible factors up to the square root of 36. However, to find all factors, you can also consider the “complementary factors” that correspond to each factor you found so far. These complementary factors are obtained by dividing 36 by each of the factors found. For example, if you found 2 as a factor, the complementary factor would be 36 divided by 2, which is 18. The complementary factors for the factors you found are:

- Complementary factor for 1: 36 ÷ 1 = 36
- Complementary factor for 2: 36 ÷ 2 = 18
- Complementary factor for 3: 36 ÷ 3 = 12
- Complementary factor for 4: 36 ÷ 4 = 9
- Complementary factor for 6: 36 ÷ 6 = 6

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

#### How many Factors of 36?

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

#### Factor Pairs of 36

The factor pairs of 36 are the pairs of numbers that, when multiplied together, result in 36. Here are the factor pairs of 36:

1 x 36 = 36

2 x 18 = 36

3 x 12 = 36

4 x 9 = 36

6 x 6 = 36

These are all the factor pairs of 36, where each pair consists of two numbers whose product is equal to 36.

#### All Factors of 36 using Multiplication

To find all the factors of 36 using multiplication, we can start with the number 1 and multiply it by different numbers until we reach the square root of 36. Here are the factors of 36 obtained through multiplication:

1 x 36 = 36

2 x 18 = 36

3 x 12 = 36

4 x 9 = 36

6 x 6 = 36

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