# Factors of 132

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

#### How to find factors of a number

 1.   Find factors of 132 using Division Method 2.   Find factors of 132 using Prime Factorization 3.   Find factors of 132 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 132

• Divide 132 by 1: 132 ÷ 1 : Remainder = 0
• Divide 132 by 2: 132 ÷ 2 : Remainder = 0
• Divide 132 by 3: 132 ÷ 3 : Remainder = 0
• Divide 132 by 4: 132 ÷ 4 : Remainder = 0
• Divide 132 by 6: 132 ÷ 6 : Remainder = 0
• Divide 132 by 11: 132 ÷ 11 : Remainder = 0
• Divide 132 by 12: 132 ÷ 12 : Remainder = 0
• Divide 132 by 22: 132 ÷ 22 : Remainder = 0
• Divide 132 by 33: 132 ÷ 33 : Remainder = 0
• Divide 132 by 44: 132 ÷ 44 : Remainder = 0
• Divide 132 by 66: 132 ÷ 66 : Remainder = 0
• Divide 132 by 132: 132 ÷ 132 : Remainder = 0

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

#### 2. Steps to find factors of 132 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 132 using the division method, follow these steps:

• Step 1. Start dividing 132 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 132, which is 2. Divide 132 by 2 to obtain the quotient (66).
132 ÷ 2 = 66
• Step 3. Repeat step 1 with the obtained quotient (66).
66 ÷ 2 = 33
33 ÷ 3 = 11
11 ÷ 11 = 1

So, the prime factorization of 132 is, 132 = 2 x 2 x 3 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 132 as shown below:

So, the prime factorization of 132 is, 132 = 2 x 2 x 3 x 11.

#### 3. Find factors of 132 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 132 would be the two numbers which, when multiplied, give 132 as the result.

The following table represents the calculation of factors of 132 in pairs:

Factor Pair Pair Factorization
1 and 132 1 x 132 = 132
2 and 66 2 x 66 = 132
3 and 44 3 x 44 = 132
4 and 33 4 x 33 = 132
6 and 22 6 x 22 = 132
11 and 12 11 x 12 = 132

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 132. They are called negative pair factors.

Hence, the negative pairs of 132 would be ( -1 , -132 ) , ( -2 , -66 ) , ( -3 , -44 ) , ( -4 , -33 ) , ( -6 , -22 ) and ( -11 , -12 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 132 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 132.
• Every number is a factor of zero (0), since 132 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132 are exact divisors of 132.
• Factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132. Each factor divides 132 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132 are all less than or equal to 132.

• How do you find factors of a negative number? ( eg. -132 )?

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

• What is the sum of all factors of 132?

The sum of all factors of 132 is 336.

• What is prime factorization of 132?

Prime factorization of 132 is 2 x 2 x 3 x 11.

• What are the pair factors of 132?

Pair factors of 132 are (1,132), (2,66), (3,44), (4,33), (6,22), (11,12).

• What are six multiples of 132?

First five multiples of 132 are 264, 396, 528, 660, 792, 924.

• Is 132 a whole number?

Yes 132 is a whole number.

• Which is the smallest prime factor of 132?

Smallest prime factor of 132 is 2.

• What are five multiples of 132?

First five multiples of 132 are 264, 396, 528, 660, 792.

• Write all factors of 132?

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

#### Examples of Factors

Joey wants to write all the prime factors of 132 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 132 are 2, 2, 3, 11.
So in exponential form it can be written as 22 x 3 x 11.

How many factors are there for 132?

Factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 132. Can you predict the answer?

11 factor(s) of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66.

Sammy is puzzled while calculating the prime factors of 132. Can you help him find them?

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

What is prime factorization of 132?

Prime factorization of 132 is 2 x 2 x 3 x 11 = 22 x 3 x 11.

Ariel has been assigned the task to find the product of all the prime factors of 132. Can you help her?

Prime factors of 132 are 2, 2, 3, 11.
Hence, the product of prime factors of 66.

Can you help Rubel to find out the product of the even factors of 132?

Factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132.
Even factors of 132 are 2, 4, 6, 12, 22, 44, 66, 132.
Hence, product of even factors of 132 is; 2 x 4 x 6 x 12 x 22 x 44 x 66 x 132 = 4857532416.