Factors of 132

The factors of 132 are the numbers that divide 132 evenly without leaving any remainder. In other words, the numbers which are multiplied together, resulting in the original number 132, are the factors of 132. The factors and the prime factors of 132 are expressed in positive and negative forms. For example, the pair factor of 132 is represented by (1, 132) or (-1, -132). If we multiply a pair of negative numbers, such as multiplying -1 and -132, it will result in the original number 132. Here, we are going to learn the factors of 132, the positive and negative pair factors of 132, and the prime factors of 132 using the prime factorization method and many solved examples.

Table of Contents:

• What are the Factors of 132?
• Pair Factors of 132
• Factors of 132 by Division Method
• Prime Factorization of 132
• Solved Examples
• FAQs

What are the Factors of 132?

In Mathematics, the numbers that divide the given number evenly without leaving any remainder are called the factors of a number. Thus, the factors of 132 are the numbers that divide 132 exactly and leave a remainder ‘0’, are the factors of 132. As the number 132 is an even composite number, it has more than two factors. Hence, the factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66 and 132. Similarly, the negative factors of 132 are -1, -2, -3, -4, -6, -11, -12, -22, -33, -44, -66 and -132.

Pair Factors of 132

A pair of numbers that are multiplied together, resulting in the original number 132, is called the pair factors of 132. As discussed above, the pair factors of 132 can be expressed in positive and negative forms. Thus, the positive and negative pair factors of 132 are given below:

Positive Pair Factors of 132:

Hence, the positive pair factors of 132 are (1, 132), (2, 66), (3, 44), (4, 33), (6, 22) and (11, 12).

Negative Pair Factors of 132:

Therefore, the negative pair factors of 132 are (-1, -132), (-2, -66), (-3, -44), (-4, -33), (-6, -22) and (-11, -12).

Factors of 132 by Division Method

In the division method, the factors of 132 are found by dividing the number 132 by different integers. If the integers divide 132 evenly, leaving a remainder 0, then those integers are the factors of 132. Now, let us discuss how to find the factors of 132 using the division method.

• 132/1 = 132 (Factor is 1 and Remainder is 0)
• 132/2 = 66 (Factor is 2 and Remainder is 0)
• 132/3 = 44 (Factor is 3 and Remainder is 0)
• 132/4 = 33 (Factor is 4 and Remainder is 0)
• 132/6 = 22 (Factor is 6 and Remainder is 0)
• 132/11 = 12 (Factor is 11 and Remainder is 0)
• 132/12 = 11 (Factor is 12 and Remainder is 0)
• 132/22 = 6 (Factor is 22 and Remainder is 0)
• 132/33 = 4 (Factor is 33 and Remainder is 0)
• 132/44 = 3 (Factor is 44 and Remainder is 0)
• 132/66 = 2 (Factor is 66 and Remainder is 0)
• 132/132 = 1 (Factor is 132 and Remainder is 0)

If we divide 132 by any numbers other than 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66 and 132, it leaves a remainder of some value. Hence, the factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66 and 132.

Prime Factorization of 132

In the prime factorization method, the number 132 is written as the product of its prime factors. The process of finding the prime factors of 132 is given below.

Take a pair factor of 132, say (1, 132). We know that the number 1 cannot be split further.

So, take the other factor, 132, which is an even composite number. Now, write the number 132 as the product of prime factors. To find the prime factorization of 132, find two numbers that on multiplication results in the original number 132.

Thus, 132 is written as the product of 11 and 12.

Now, 11 is a prime number and 12 is a composite number, which is further factored into 4 × 3, equal to 2 × 2 × 3.

Thus, the prime factorization of 132 is 2 × 2 × 3 × 11 or 2² × 3 × 11, where 2, 3 and 11 are prime numbers.

Video Lesson on Prime Factors

Solved Examples

Example 1:

Find the common factors of 132 and 131.

Solution:

The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66 and 132.

The factors of 131 are 1 and 131.

As 131 is a prime number, the common factor of 132 and 131 is 1.

Example 2:

What are the common factors of 132 and 133?

Solution:

Factors of 132 = 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66 and 132.

Factors of 133 = 1, 7, 19 and 133.

Thus, the common factor of 132 and 133 is 1.

Example 3:

Find the common factors 132 and 66.

Solution:

The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66 and 132.

The factors of 66 are 1, 2, 3, 6, 11, 22, 33 and 66.

Therefore, the common factors of 132 and 66 are 1, 2, 3, 6, 11, 22, 33 and 66.