Factors of 120 using Prime Factorization
The Factors of 120
What are the factors of 120?
The factors of 120 are those integers that divide 120 without leaving any remainder. For example, 6 is a factor of 120 because when we divide 120 by 6, it leaves the remainder equal to 0. Moreover, 20, which appears as a quotient in the above division, is also a factor of 120.
So, to check if any number is a factor of 120 or not, divide 120 by that number and verify whether the remainder is zero or not.
Factor List of 120
The factors of 120 can be obtained by divisibility rules and division facts.
So the factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
The Prime Factors of 120
The number 120 is a composite number, that is, it has more than two factors. A factor tree can be used to obtain the prime factors or prime factorization of 120.
Therefore, the prime factorization of 120 is 2 x 2 x 2 x 3 x 5 or \(2^3\) x 3 x 5.
So 2, 3, and 5 are the prime factors of 120.
The Factor Pairs of 120
The factor pair of a number is a set of two factors whose product is the number itself.
Example: (2, 60) is the factor pair of 120.
The factor pair can be a positive pair or a negative pair.
Positive Pair Factors of 120
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Rapid Recall
The factors of 120 are:
Solved Examples
Example 1: Find the common factors of 30 and 120.
Solution :
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
So, the common factors of 30 and 120 are 1, 2, 3, 5, 6, 10, 15, and 30.
Example 2: Find the greatest common factor of 93 and 120.
Solution :
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
Factors of 93: 1, 3, 31, and 93.
So, the greatest common factor of 93 and 120 is 3.
Example 3: A florist has 120 flowers and 10 vases. He wants to put an equal number of flowers in each vase. How many flowers will he put in each vase?
Solution:
Total number of flowers = 120
Number of vases = 10
The number of flowers in each vase will be equal to the total number of flowers divided by the number of vases, that is,
\(\frac{120}{10}\)
= \(\frac{120~\times~10}{10}\) [(12, 10) is a factor pair of 120]
= 12 [Divide the numerator and the denominator by 10]
Therefore, the florist should place 12 flowers in each vase so that each vase has an equal number of flowers.
When you divide 120 by 45, it will leave 3 as a quotient and 30 as a remainder. So, 120 is not evenly divisible by 45. Hence, 45 is not a factor of 120.
The numbers that divide 120 evenly, that is, leave a zero remainder are known as factors of 120.
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
So, 120 has a total of 16 factors.
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
Common factors of 90 and 120 are 1, 2, 3, 5, 6, 10, 15, 30.
So, the greatest common factor is 30.