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Factors of 120 are the numbers that give the number 120 as the product on multiplication with each other. The numbers that divide 120 completely without leaving any remainder are referred to as the factors of 120. The number 120 has a total of 16 factors. The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12,15, 20, 24, 30, 40, 60, and 120. The biggest factor of 120 is 120 itself and 2, 3, and 5 are the prime factors of 120. The factors of 120 can be found through the division method as well as prime factorization. The sum of all the factors of 120 is 360.
Key Terms: Factors of 120, Pair Factors, Prime Factors, Prime Numbers, Remainder, Multiplication, Prime Factorization
What are Factors of 120?
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Factors of 120 are the natural numbers that leave zero as the remainder on division with 120. They are the numbers that when multiplied together give 120 as the product. The number 120 is a composite number, thus, it has more than two factors which include both prime and composite numbers.
| Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12,15, 20, 24, 30, 40, 60, 120 |
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Factors of 120 in Pairs
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Pair factors of 120 are the two numbers that give the original number 120 as the product on multiplication with each other. The pair factors of 120 can be positive as well as negative. Since the product of two negative numbers will also give the positive value of 120, thus, it can have negative factors also. The positive and negative pair factors of 120 are as follows:
Positive Pair Factors of 120
The positive pair factors of 120 are as follows:
| 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) |
Negative Pair Factors of 120
The negative pair factors of 120 are listed below:
| 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
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120 is a composite number, thus, it surely has prime factors. The prime factorization of 120 is used to find the prime factors of 120. The step-by-step procedure for the prime factorization of 120 is as follows:
Step 1: Divide the number 120 by 2 as 2 is the smallest prime number. Continue this division until we get a decimal number or 1.
120 ÷ 2 = 60
60 ÷ 2 = 30
30 ÷ 2 = 15
Step 2: Since we have got a decimal number, the number just above the decimal has to be divided with another prime number followed by 2. The next prime number is 3.
15 ÷ 3 = 5
Step 3: Now, 5 is not divisible by 3, so the next prime number 5.
5 ÷ 5 = 1
Thus, 1 is obtained at the end of the division process. Thus, we will not proceed further. The prime factorization of 120 is 120 = 2 × 2 × 2 × 3 × 5. It can also be written as 120 = 2³ x 3 × 5. Thus, the prime factors of 120 are 2, 3, and 5.
Read More: Co-Prime Numbers
Factors of 120 Using Multiplication
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Factors of 120 can be found through multiplication as well. In this method, we need to check which two numbers give 120 as the product on multiplication with each other. Through this method, we will get the factors of 120 starting from 1 up to 120.
- 1 × 120 = 120
- 2 × 60 = 120
- 3 × 40 = 120
- 4 × 30 = 120
- 5 × 24 = 120
- 6 × 20 = 120
- 8 × 15 = 120
- 10 × 12 = 120
Thus, the factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12,15, 20, 24, 30, 40, 60, and 120.
Read More: Multiplication and Division of Integers
Factor Tree of 120
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The prime factors of 120 can also be found using the factor tree method. The factor tree of 120 is drawn by factorizing 120 until we get the prime factors at the end of its branches. Factor tree of 120 includes the factors being split and written in the form of the branches of a tree.
Factor Tree of 120 is given as follows:
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Solved Examples on Factors of 120
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| Example 1: State the common factors of 120 and 30. Solution: First, we will write down all the factors of 120 and 30
Thus, the common factors of 120 and 30 are 1, 2, 3, 5, 6, 10, 15, and 30. Example 2: What is the greatest common factor of 93 and 120? Solution: Listing all the factors of 120 and 93, we get
The common factors of 93 and 120 are 1, and 3. Thus, the greatest common factor of 93 and 120 is 3. |
Things to Remember
- Factors of 120 are the numbers that leave no remainder on dividing 120.
- Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
- The prime factorization of 120 is 120 = 2 × 2 × 2 × 3 × 5 or 2³ x 3 × 5.
- 2, 3, and 5 are the three prime factors of 120.
- The positive pair factors of 120 are (1, 120), (2, 60), (3, 40), (4, 30), (5, 24), and (6, 20), (8, 15), (10, 12).
- The negative pair factors of 120 are (-1, -120), (-2, -60), (-3, -40), (-4, -30), (-5, -24), and (-6, -20), (-8, -15), (-10, -12).
Sample Questions
Ques. Find out the highest common factor (HCF) of the numbers 120 and 60. (2 Marks)
Ans. We know that,
- Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
- Factors of 60 = 1, 2, 4, 5, 6, 10,12, 20, 30, 60.
The common factors of 120 and 60 are 1, 2, 4, 5, 10,12, 20, 30, and 60. Hence, the Greatest Common Factor (GCF) of 120 and 60 is 60.
Ques. Find the sum of all the factors of 120. (2 Marks)
Ans. The sum of all the factors of 120 can be calculated by adding all the factors of 120 which are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 20 + 24 + 30 + 40+ 60 + 120 = 360.
Thus, the sum of the factors of 120 is 360.
Ques. What are the common factors of 120 and 80? (2 Marks)
Ans. The factors of 120 and 80 are
- Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
- Factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.
Hence, the common factors of 120 and 80 are 1, 2, 4, 8, 10, 20, and 40.
Ques. How many numbers of factors does the number 120 have? (1 Mark)
Ans. The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Thus, the number 120 has a total of 16 factors.
Ques. What are the prime factors of 120? (2 Marks)
Ans. The prime factorization of 120 is given as
120 = 2 × 2 × 2 × 3 × 5
It can be simplified as 120 = 2³ × 3 × 5
Thus, the prime factors of 120 are 2,3 and 5.
Ques. Is 80 a factor of 120? (2 Marks)
Ans. In order to find out whether 80 is a factor of 120, we will divide 120 by 80. If the remainder is zero, 80 is the factor of 120.
120 ÷ 80 = 1.5
1.5 is a decimal number. The remainder is not zero, thus, 80 is not a factor of 120.
Ques. What are the negative pairs of 120 and how do we obtain them? (2 Marks)
Ans. The negative pairs of 120 are (-1×-120), (-2×-60), (-3×-40), (-4×-30), (-5×-24), (-6×-20), (-8×-15), and (-10×-12). The negative factors of 120 can be obtained by simply putting negative signs before the factors of 120. As the number 120 is positive, both the numbers in the pairs have to be negative to get the positive number as the answer.
Ques. What is the highest common factor of 70 and 120? (2 Marks)
Ans. Writing down all the factors of 70 and 120, we get
- Factors of 70 = 1,2,5,10,14,35, 70
- Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The common factors of 120 and 70 are 1, 2, 5, and 10. Thus, the highest common factor is 10.
Ques. Is 40 a factor of 120? (2 Marks)
Ans. In order to find out whether 40 is a factor of 120, we have to divide 120 by 40.
120 ÷ 40 = 30
Since the remainder is zero, 40 is a factor of 120.
Ques. Find the common factors of 100 and 120. (2 Marks)
Ans. The factors of 100 and 120 are
- Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
- Factors of 100 = 1, 2, 4, 5,10, 20, 25, 50, and 100.
Thus, the common factors are 1, 2, 4, 5, 10, and 20.
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