Factor of 132 Using Prime Factorization
What are the Factors of 132?
The factors of 132 are numbers that divide 132 without leaving any remainder.
For Example:
Dividing 132 by 2 yields a quotient of 66 and a remainder of 0, which means that 2 is a factor of 132. Also, the quotient 66 is a factor of 132.
To determine whether or not a number is a factor of 132, divide 132 by that number, and if the remainder is zero, the number is said to be a factor of 132.
Factor List of 132
Prime Factorization of 132
132 is a composite number, that is, it has more than two factors. Prime factorization is the process of expressing the composite number as the product of its prime factors.
To carry out the prime factorization of 132, we will keep dividing 132 by its prime factors, until we get the result as 1.
As 132 is even, let’s start dividing by 2.
132 ÷ 2 = 66
66 ÷ 2 = 33
Now, divide 33 by 3,
33 ÷ 3 = 11
11 is a prime number itself, so we will divide 11 by 11;
11 ÷ 11 = 1
So, the prime factorization of 132 = 2 × 2 × 3 × 11 or \(2^2\) × 3 × 11.
Hence the factor tree of 132 can be written as:
Factor Pairs of 132
Factor pairs of 132 are different sets that contain two factors of 132. When these pairs are multiplied together, the product is 132.
For example, (3, 44) is a factor pair of 132, as 3 \(\times\) 44 = 132 and both 3 and 44 are factors of 132.
Solved Examples
Example 1: Find the factors common between 88 and 132.
Solution:
Factors of 88 = 1, 2, 4, 8, 11, 22, 44 and 88
Factors of 132 = 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66 and 132
Therefore, the factors common between 88 and 132 are 1, 2, 4, 11, 22 and 44.
Example 2: Is 9 a factor of 132?
Solution:
\(\frac{132}{9}\) = 14 R6
So, 9 is not a factor of 132. As the number 9 does not divide 132 exactly. It leaves a remainder of 6. Additionally, the sum of the digits of 132, which is 6, is not divisible by 9.
Example 3: A train from Unicorn Village has to travel 132 miles to reach Fairy Land. In one hour the train covers 33 miles. When the train completes travelling for an hour, two trains start from Fairy Land to Unicorn Village. How many trains start from Fairy Land to Unicorn Village during this time?
Solution:
Total distance to be covered = 132 miles
Distance covered in one hour = 33 miles
Time taken to travel 132 miles = \(\frac{132}{33}\) = 4 hours
For every hour the train completes, 2 trains start in the opposite direction.
Hence, the number of trains that travel from Fairy Land to Unicorn Village = 4 \(\times\) 2 = 8
Therefore, eight trains start from Fairy Land to Unicorn Village in four hours.
The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66 and 132
So, the least factor of 132 is 1 and the greatest factor is 132 itself.
The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66 and 132.
Sum of this set of factors = 1 + 2 + 3 + 4 + 6 + 11 + 12 + 22 + 33 + 44 + 66 + 132 = 336
Hence, the sum of the factors of 132 is 336.
A factor of 132 is a natural number that evenly divides 132, leaving zero as the remainder. Whereas a multiple of 132 is a number obtained by multiplying a natural number with 132.