Factors of 132

The numbers that divide 132 evenly are known as factors of 132. A factor of 132 is a number that divides the number without remainder. The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132.

Negative factors of 132: -1, -2, -3, -4, -6, -11, -12, -22, -33, -44, -66, and -132.

Prime factors of 132: 2, 3, and 11.

Prime factorization of 132: 2² × 3 × 11.

The sum of factors of 132: 1 + 2 + 3 + 4 + 6 + 11 + 12 + 22 + 33 + 44 + 66 + 132 = 336

Factors can be found using different methods. Mentioned below are some commonly used methods:

1. Finding factors using multiplication
2. Finding factors using the division method
3. Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 132. Identifying the numbers which are multiplied to get the number 132 is the multiplication method.

Step 1: Multiply 132 by 1, 132 × 1 = 132.

Step 2: Check for other numbers that give 132 after multiplying 2 × 66 = 132

3 × 44 = 132

4 × 33 = 132

6 × 22 = 132

11 × 12 = 132

Therefore, the positive factor pairs of 132 are: (1, 132), (2, 66), (3, 44), (4, 33), (6, 22), (11, 12). For every positive factor, there is a negative factor.

Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following simple division method -

Step 1: Divide 132 by 1, 132 ÷ 1 = 132.

Step 2: Continue dividing 132 by the numbers until the remainder becomes 0.

132 ÷ 1 = 132

132 ÷ 2 = 66

132 ÷ 3 = 44

132 ÷ 4 = 33

132 ÷ 6 = 22

132 ÷ 11 = 12

Therefore, the factors of 132 are: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132.

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

• Using prime factorization
• Using factor tree

Using Prime Factorization: In this process, prime factors of 132 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

132 ÷ 2 = 66

66 ÷ 2 = 33

33 ÷ 3 = 11

11 ÷ 11 = 1

The prime factors of 132 are 2, 3, and 11. The prime factorization of 132 is: 2² × 3 × 11.

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 132 is divided by 2 to get 66.

Step 2: Now divide 66 by 2 to get 33.

Step 3: Then divide 33 by 3 to get 11. Here, 11 is a prime number, that cannot be divided anymore. So, the prime factorization of 132 is: 2² × 3 × 11.

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

• Positive factor pairs of 132: (1, 132), (2, 66), (3, 44), (4, 33), (6, 22), and (11, 12).
• Negative factor pairs of 132: (-1, -132), (-2, -66), (-3, -44), (-4, -33), (-6, -22), and (-11, -12).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132.

• Prime factors: The factors which are prime numbers. For example, 2, 3, and 11 are prime factors of 132.

• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 132 are (1, 132), (2, 66), etc.

• Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to the given number.

• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 132 is 2^2 × 3 × 11.