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Factors of 132: Prime Factorization, Methods, and Examples
Factors of 132 are the integers that evenly divide 132 without leaving anything behind. 132 is an even number which means that it is divisible by 2 and its smallest prime factor is also 2. There are 12 factors of 132 in total and 132 is the biggest factor of number 132.
Factors of 132
Here are the factors of number 132.
Factors of 132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132
Negative Factors of 132
The negative factors of 132 are similar to its positive factors, just with a negative sign.
Negative Factors of 132: -1, -2, -3, -4, -6, -11, -12, -22, -33, -44, -66, and -132
Prime Factorization of 132
The prime factorization of 132 is the way of expressing its prime factors in the product form.
Prime Factorization: 2 x 2 x 3 x 11
In this article, we will learn about the factors of 132 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 132?
The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132. All of these numbers are the factors as they do not leave any remainder when divided by 132.
The factors of 132 are classified as prime numbers and composite numbers. The prime factors of the number 132 can be determined using the prime factorization technique.
How To Find the Factors of 132?
You can find the factors of 132 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.
To find the factors of 132, create a list containing the numbers that are exactly divisible by 132 with zero remainders. One important thing to note is that 1 and 132 are the 132’s factors as every natural number has 1 and the number itself as its factor.
1 is also called the universal factor of every number. The factors of 132 are determined as follows:
\[\dfrac{132}{1} = 132\]
\[\dfrac{132}{2} = 66\]
\[\dfrac{132}{3} = 44\]
\[\dfrac{132}{4} = 33\]
\[\dfrac{132}{11} = 12\]
\[\dfrac{132}{12} = 12\]
\[\dfrac{132}{22} = 6\]
\[\dfrac{132}{33} = 4\]
\[\dfrac{132}{44} = 3\]
\[\dfrac{132}{66} = 2\]
\[\dfrac{132}{132} = 1\]
Therefore, 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132 are the factors of 132.
Total Number of Factors of 132
For 132 there are 12 positive factors and 12 negative ones. So in total, there are 24 factors of 132.
To find the total number of factors of the given number, follow the procedure mentioned below:
- Find the factorization/prime factorization of the given number.
- Demonstrate the prime factorization of the number in the form of exponent form.
- Add 1 to each of the exponents of the prime factor.
- Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.
By following this procedure the total number of factors of 132 is given as:
Factorization of 132 is 1 x 2$^2$ x 3 x 11.
The exponent of 1, 3, and 11 is 1. The exponent of 2 is 2
Adding 1 to each and multiplying them together results in 24.
Therefore, the total number of factors of 132 is 24. 12 are positive and 12 factors are negative.
Important Notes
Here are some important points that must be considered while finding the factors of any given number:
- The factor of any given number must be a whole number.
- The factors of the number cannot be in the form of decimals or fractions.
- Factors can be positive as well as negative.
- Negative factors are the additive inverse of the positive factors of a given number.
- The factor of a number cannot be greater than that number.
- Every even number has 2 as its prime factor which is the smallest prime factor.
Factors of 132 by Prime Factorization
The number 132 is a composite. Prime factorization is a useful technique for finding the number’s prime factors and expressing the number as the product of its prime factors.
Before finding the factors of 132 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.
To start the prime factorization of 132, start dividing by its smallest prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.
Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 132 can be expressed as:
132 = 2 x 2 x 3 x 11
Factors of 132 in Pairs
The factor pairs are the duplet of numbers that when multiplied together result in the factorized number. Depending upon the total number of factors of the given numbers, factor pairs can be more than one.
For 132, the factor pairs can be found as:
1 x 132 = 132
2 x 66 = 132
3 x 44 = 132
4 x 33 = 132
6 x 22 = 132
11 x 22 = 132
The possible factor pairs of 132 are given as (1, 132), (2, 66), (3, 44), (4, 33), (6, 22), and (11, 12 ).
All these numbers in pairs, when multiplied, give 132 as the product.
The negative factor pairs of 132 are given as:
-1 x -132 = 132
-2 x -66 = 132
-3 x -44 = 132
-4 x -33 = 132
-6 x -22 = 132
-11 x -22 = 132
It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign due to which the resulting product is the original positive number. Therefore, -1, -2, -3, -4, -6, -11, -12, -22, -33, -44, -66, and -132 are called negative factors of 132.
The list of all the factors of 132 including positive as well as negative numbers is given below.
Factor list of 132: 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 11, -11, 12, -12, 22, -22, 33, -33, 44, -44, 66, -66, 132, and -132
Factors of 132 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 132 are there?
Solution
The total number of Factors of 132 is 12.
Factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132.
Example 2
Find the factors of 132 using prime factorization.
Solution
The prime factorization of 132 is given as:
132 $\div$ 2 = 66
66 $\div$ 2 = 33
33 $\div$ 3 = 11
11 $\div$ 11 = 1
So the prime factorization of 132 can be written as:
2 x 2 x 3 x 11 = 132