Factors of 120, using Prime Factorization Methods

Factors of 120

The factors of 120 are all the numbers, when multiplied together in a pair of two, give the number 120. For example, the two numbers let’s say x and y when these two numbers are multiplied together and their results will be 120 then these two numbers are called the factors of 120. In this article, we will learn about the factors of 120. The students can calculate the factors of other numbers with the help of the method provided on this page. 

Factors of 120 in pairs

The factors of 120 refer to the number of factors which are multiple of 120 and two factors when multiplied together gives 120 as a result. Below, we have given the factors of 120 and the prime factorization of 120 check them out. 

Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120

Prime Factorization of 120: 2³×3×5

Positive Factors of 120

In the below table we have given the pair factors of 120. The pair factors of 120 can be determined by multiplying two numbers in a pair to get the original number. Pair factors can be positive or negative. In the below table, we have given the positive pair factors of 120.

Negative Factors of 120

In the below table we have given the negative factors of 120. Check out the below table and check the negative pair factors of 120. To be a negative factor both the multiple of 120 should be negative. Have a look at the table below to know the negative factors of 120.

Solved Examples for Factors of 120

The students must solve the questions of factors of 120. Maths is all about practice, one can not ace maths without practice. To ease of students we have given some solved examples, the students must try to solve these examples without looking at their solutions. If students are unable to solve a question then they can see the solution and try to solve different questions given on the internet and maths books. Have a look at the solved examples given below:

Q. Find the common factors of 120 and 60.

Solution:

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

The factors of 60 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60.

60 itself is the factor of 120 so the common factors of 120 and 60 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60. Hence, 60 and 12 have 15 common factors.

Q. Find the common factors of 120 and 117.

Solution:

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

The factors of 117 are 1, 3, 9, 13, 39, 117.

Therefore, the common factor of 120 and 117 is 1, 3.

Hence, 120 and 117 have 2 common factors.

Q. Find the common factors of 120 and 115.

Solution:

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

The factors of 115 are 1, 5, 23, and 115.

Therefore, the common factor of 120 and 115 is 1, 5.

Hence, 120 and 115 have 2 common factors.

Q. Find the common factors of 120 and 123.

Solution:

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

The factors of 123 are 1, 3, 41, 123.

Therefore, the common factor of 120 and 123 is 1, 3.

Hence, 120 and 123 have 2 common factors.

Q. Find the common factors of 120 and 98.

Solution:

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

The factors of 98 are 1, 2, 7, 14, 49, and 98

Therefore, the common factor of 120 and 98 is 1, 2.

Hence, 120 and 98 have 2 common factors.

Q. Find the common factors of 120 and 82.

Solution:

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

The factors of 82 are 1, 2, 41, and 82.

Therefore, the common factor of 120 and 82 is 1, 2.

Hence, 120 and 82 have 2 common factors.

Q. Find the common factors of 120 and 78.

Solution:

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, and 78.

Therefore, the common factor of 120 and 78 is 1, 2, 3.

Hence, 120 and 78 have 3 common factors.

Q. Find the common factors of 120 and 24.

Solution:

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

The factors of 24 are 1, 2, 3, 4, 6, 12, and 24.

Therefore, the common factor of 120 and 24 is 1, 2, 3, 4, 6, 12, 24.

Hence, 120 and 24 have 7 common factors. 24 itself is a factor of 120.

Q. Find the common factors of 120 and 72.

Solution:

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72

Therefore, the common factor of 120 and 72 is 1, 2, 3, 4, 6, 8, 12, 24.

Hence, 120 and 72 have 8 common factors.

Q. Find the common factors of 120 and 96.

Solution:

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.

Therefore, the common factor of 120 and 96 is 1, 2, 3, 4, 6, 8, 12, 24.

Hence, 120 and 96 have 8 common factors.

Q. Find the common factors of 120 and 66.

Solution:

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

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

Therefore, the common factor of 120 and 66 is 1, 2, 3, 6.

Hence, 120 and 66 have 4 common factors.

Q. Find the common factors of 120 and 144.

Solution:

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

The factors of 144 are 1, 4, 2, 3, 6, 8, 16, 9, 12, 18, 24, 36, 48, 72, 144.

Therefore, the common factor of 120 and 144 is 1, 4, 2, 3, 6, 8, 12, 24.

Hence, 120 and 144 have 8 common factors.

Q. Find the common factors of 120 and 240.

Solution:

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, and 240.

Therefore, the common factor of 120 and 240 is 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

Hence, 120 and 240 have 16 common factors and 120 itself is one of the factors of 240.

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