Factors of 120

Factors of 120 are those numbers that divide 120 completely without leaving any remainder. There are 16 factors of 120 among which 120 is the biggest factor and 2, 3 and 5 are its prime factors. The prime factorization of 120 can be done by multiplying all its prime factors such that the product is 120. Let us learn about all factors of 120, the prime factorization of 120, and the factor tree of 120 in this article.

The factors of 120 can be listed as 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. According to the definition of factors, the factors of 120 are those numbers that divide 120 without leaving any remainder. In other words, if two numbers are multiplied and the product is 120, then the numbers are the factors of 120. It means that 120 is completely divisible by all these numbers. Apart from these, 120 also has negative factors that can be listed as, -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -20, -24, -30, -40, -60 and -120.. For negative factors, we need to multiply a negative factor by a negative factor, like, (-40) × (-3) = 120.

Factorization of a number means writing the number as a product of its factors. The multiplication method is the most commonly used method to find the factors of a number. Let us find the factors of 120 using multiplication.

All Factors of 120 using Multiplication

Let us find all factors of 120 using the multiplication method using the following steps.

• Step 1: In order to find the factors of 120 using multiplication, we need to check what pairs of numbers multiply to get 120, so we need to divide 120 by natural numbers starting from 1 and go on till 9. We need to make a note of those numbers that divide 120 completely.
• Step 2: The numbers that completely divide 120 are known as its factors. We write that particular number along with its pair and make a list as shown in the figure given above. As we check and list all the numbers up to 9, we automatically get the other pair factor along with it. For example, starting from 1, we write 1 × 120 = 120, and 2 × 60 = 120 and so on. Here, (1, 120) forms the first pair, (2, 60) forms the second pair and the list goes on as shown. So, as we write 1 as the factor of 120, we get the other factor as 120; and as we write 2 as the factor of 120, we get 60 as the other factor. Like this, we get all the factors.
• Step 3: After the list is noted, we get all the factors of 120 starting from 1 up there, coming down and then we go up again up to 120. This gives us a complete list of all the factors of 120 as shown in the figure given above.

Therefore, the factors of 120 can be listed as 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Now, let us learn about the prime factorization of 120.

Prime Factors of 120

The prime factors of 120 are those factors of 120 that are prime numbers. The prime factors of 120 are different from the factors of 120. As we saw in the section above, the factors of 120 can be listed as 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. However, all of these are not prime numbers. So, let us find the prime factors of 120 using prime factorization in the following section.

Prime factorization is a way of expressing a number as a product of its prime factors. The prime factors of a number are those factors that are prime numbers. The prime factorization of 120 can be done using the following steps. Observe the figure given below to understand the prime factorization of 120.

• Step 1: The first step is to divide the number 120 with its smallest prime factor. We know that a prime factor is a prime number which is a factor of the given number. So, with the help of divisibility rules, we find out the smallest factor of the given number. Here, we get 2. Therefore, 2 is the smallest prime factor of 120. So, 120 ÷ 2 = 60
• Step 2: We need to repeatedly divide the quotient by 2 until we get a number that is no more divisible by 2. So, we divide 60 again by 2 which is 60 ÷ 2 = 30. We again divide 30 by and get 30 ÷ 2 = 15
• Step 3: Now, 15 is not completely divisible by 2, so, we proceed with the next prime factor of 120, which is 3. So we will divide 15 by 3, that is, 15 ÷ 3 = 5
• Step 5: Since 5 is a prime number it will be divided by 5 and we will get 1 as the quotient.
• Step 6: We need not proceed further as we have obtained 1 as our quotient.
• Step 7: Therefore, the prime factorization of 120 is expressed as 2 × 2 × 2 × 3 × 5 = 2³ × 3 × 5; where 2, 3, and 5 are prime numbers and the prime factors of 120.

Therefore, the prime factors of 120 are 2, 3, and 5 and the prime factorization of 120 = 2 × 2 × 2 × 3 × 5

We can also find the prime factors of 120 using a factor tree. The factor tree of 120 can be drawn by factorizing 120 until we reach its prime factors. These factors are split and written in the form of the branches of a tree. The final factors are circled and are considered to be the prime factors of 120. Let us find the prime factors of 120 using the following steps and the factor tree given below.

• Step 1: Split 120 into two factors. Let us take 2 and 60.
• Step 2: Observe these factors to see if they are prime or not.
• Step 3: Since 2 is a prime number we circle it as one of the prime factors of 120. We move on to 60, which is a composite number and further split it into more factors. In other words, we repeat the process of factorizing the composite numbers and splitting it into branches until we reach a prime number.
• Step 4: After factorizing 60, we get 2 and 30. So, we circle 2 because it is a prime number and we split 30 into 2 and 15. Then, we circle 2 and split 15 into 3 and 5. At this stage, we are left with prime numbers, 2, 3, and 5. We circle them since we know that they cannot be factorized further. This is the end of the factor tree.
• Step 5: Therefore, the prime factors of 120 = 2 × 2 × 2 × 3 × 5

Note: It should be noted that there can be different factor trees of 120. For example, we can start by splitting 120 into 3 and 40. Since 3 is already a prime number, we circle it and then we split 40 further into 2 and 20. Again, we get 2 as the prime number, so we circle it and split 20 into 2 and 10. Then we circle 2 and split 10 into 2 and 5. Finally, we can observe the same prime factors, that is, 120 = 2 × 2 × 2 × 3 × 5

The factors of 120 can be written in pairs. This means that the product of the pair factors of 120 is always 120. The factors of 120 in pairs can be written as shown in the table given below:

It is possible to have negative pair factors as well because the product of two negative numbers also gives a positive number. Let us have a look at the negative pair factors of 120.

The following points explain some features of the pair factors of 120.

• The pair factors of the number 120 are whole numbers in pairs that are multiplied to get the original number, i.e.,120.
• Pair factors could be either positive or negative but they cannot be fractions or decimal numbers.
• The positive pair factors of 120 are as follows: (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)

Important Notes

• Only composite numbers can have more than two factors. Since 120 is a composite number, it has more than two factors.
• Factors of 120 are those numbers that divide 120 completely without leaving any remainder.
• 120 has a total of 16 factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
• There is a trick to calculate the total number of factors of a number. For example, 120 = 2 × 2 × 2 × 3 × 5 = 2³ × 3 × 5. We get the prime factorizations of 120 as 2³ × 3 × 5. Just add one (1) to the exponents 3, 1 and 1 individually and multiply their sums. (3 + 1) × (1 + 1) × (1 + 1) = 4 × 2 × 2 = 16. This means 120 has 16 factors in all.

Points to remember

Let us recollect the list of the factors, the negative factors, and the prime factors of 120.

• Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120
• Negative Factors of 120: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -20, -24, -30, -40, -60 and -120
• Prime Factors of 120: 2, 3, 5
• Prime Factorization of 120: 2 × 2 × 2 × 3 × 5 = 2³ × 3 × 5

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What are all the Factors of 120?

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

What are the Prime Factors of 120?

The prime factors of 120 are 2, 3, and 5. The prime factors of a number are those factors that are prime numbers. In this case, if we do the prime factorization of 120, we get 2 × 2 × 2 × 3 × 5 = 2³ × 3 × 5, where 2, 3, and 5 are prime numbers and the prime factors of 120.

What is the Greatest Common Factor of 120 and 80?

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 and the factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80. The common factors of 120 and 80 are 1, 2, 4, 8, 10, 20, and 40. Hence, the Greatest Common Factor (GCF) of 120 and 80 is 40.

What is the Sum of Factors of 120?

The sum of all the factors of 120 can be calculated by adding 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120 which is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 20 + 24 + 30 + 40+ 60 + 120 = 360.

What are the Common Factors of 120 and 160?

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 and the factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160. The common factors of 120 and 160 are 1, 2, 4, 5, 8, 10, 20, and 40.

How many Multiples of 5 are Factors of 120?

Among the factors of 120, the multiples of 5 are 5, 10, 15, 20, 30, 40, 60 and 120. This means these 8 multiples of 5 are among the factors of 120.

Find the Number of Factors of 120.

120 has 16 factors that can be listed as, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. There is a trick to calculate the total number of factors of a number. For example, we know the prime factorizations of 120 as 2³ × 3 × 5. We just need to add one (1) to the exponents 3, 1 and 1 individually and multiply their sums. This leads to (3 + 1) × (1 + 1) × (1 + 1) = 4 × 2 × 2 = 16. This means 120 has 16 factors in all.

How many Factors does 120 Have?

120 has a total of 16 factors that can be listed as, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. However, the prime factors of 120 are 2, 3, and 5.

What is the Prime factorization of 120?

The prime factorization of 120 is expressed as follows: prime factorization of 120 = 2 × 2 × 2 × 3 × 5. It is to be noted that prime factorization is a way of expressing a number as a product of its prime factors. The prime factors of a number are those factors that are prime numbers. Here, 2, 3, and 5 are prime numbers and the prime factors of 120.