Factors of 120 are the numbers, which gives the result as 120 when multiplied together in a pair. There are many factors that are commonly used in mathematical calculations such as factors of 56, 90, etc. Prime factors of number 120 basically give out prime numbers. To find the factors of a number, 120, we will use the division method. Here we will find the factors in pair, total factors and the prime factorization of 120.
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What are the Factors of 120?
The factors of 120 are the numbers that divide the number 120 exactly without leaving any remainder. In other words, the numbers which on multiplication in pairs resulting in the original number 120, are called the factors of 120. As 120 is a composite number, it has more than two factors. The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.
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 |
Pair Factors of 120
We can find the pair factors of a number 120, by multiplying two numbers in a pair to get the original number. The pair factors of 120 can be positive or negative. The following are the positive and negative pair factors of 120.
Positive Factors of 120 | Positive Pair Factors of 120 |
1 × 120 | (1, 120) |
2 × 60 | (2, 60) |
3 × 40 | (3, 40) |
4 × 30 | (4, 30) |
5 × 24 | (5, 24) |
6 × 20 | (6, 20) |
8 × 15 | (8, 15) |
10 × 12 | (10, 12) |
Likewise, the negative pair factors of 120 are:
Negative Factors of 120 | Negative Pair Factors of 120 |
-1 × -120 | (-1, -120) |
-2 × -60 | (-2, -60) |
-3 × -40 | (-3, -40) |
-4 × -30 | (-4, -30) |
-5 × -24 | (-5, -24) |
-6 × -20 | (-6, -20) |
-8 × -15 | (-8, -15) |
-10 × -12 | (-10, -12) |
Prime Factorization of 120
120 is a composite number. Now let us find the prime factors of 120.
The first step is to divide the number 120 with the smallest prime factor, i.e. 2 and continue dividing by 2 until you get a fraction.
120 ÷ 2 = 60
60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 2 = 7.5; 7.5 cannot be a factor
Now, proceed to the next prime numbers, i.e. 3 and continue dividing till you get a fraction or 1.
15 ÷ 3 = 5
5 ÷ 3 = 1.66; cannot be a factor
Therefore, moving to the next prime number, 5.
5 ÷ 5 = 1
We have received 1 at the end of the division process and further, we cannot proceed. So, the prime factors of 120 are 2 × 2 × 2 × 3 × 5 or 23 × 3 × 5, where 2, 3 and 5 are the prime numbers.
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Examples
Example1:
Find the common factors of 120 and 121.
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 121 are 1, 11 and 121.
Therefore, the common factor of 120 and 121 is 1.
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Example 2:
Find the common factors of 120 and 119.
Solution:
Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120
Factors of 119 = 1, 7, 17, 119.
Therefore, the common factor of 120 and 119 is 1.
Example 3:
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, 10, 12, 15, 20, 30, and 60.
Hence, the common factors of 120 and 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
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Frequently Asked Questions on Factors of 120
What are the factors of 120?
The factors of 120 are the numbers which are multiplied in pairs, resulting in the original number 120. The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.
What is the prime factorization of 120?
The prime factorization of 120 is 2 × 2 × 2 × 3 × 5 or 23 × 3 × 5.
What are the positive pair factors of 120?
The positive pair factors of 120 are (1, 120), (2, 60), (3, 40), (4, 30), (5, 24), (6, 20), (8, 15), and (10, 12).
Write down the negative pair factors of 120?
The negative pair factors of 120 are (-1, -120), (-2, -60), (-3, -40), (-4, -30), (-5, -24), (-6, -20), (-8, -15), and (-10, -12).
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Is 60 a factor of 120?
Yes, 60 is a factor of 120. As the number 60 divides 120 exactly without leaving any remainder, 60 is a factor of 120.
Quiz on Factors of 120
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