How to find the number of factors of 120

Factors of 120 are numbers that, when multiplied together in a pair, produce the value of 120. Many factors, such as 56, 90, and so on, are often utilised in mathematical computations. The prime factors of the integer 120 produce prime numbers. 

We’ll use the division method to get the factors of a number, 120. The factors in pairs, total factors, and the prime factorisation of 120 may be found here.

  • Total Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120  
  • Negative Elements: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -20, -24, -30, -40, -60, and -120 are all possible values.
  • Most Important Prime Factorisation of 120: 2 × 2 × 2 × 3 × 5 = 23 × 3 × 5
  • The sum of the 120 factors is 360.

What Are the 120 Factors?

Integers that divide 120 without leaving a remainder are known as factors of 120. For example, 10 divides 120 without leaving any residue; hence it is a factor of 120. Surprisingly, the quotient of the previous division, 12, is likewise a factor of 120. 

Divide 120 by 12 using a long division to see if you get 0 as a leftover.

How will you find all the Factors of 120?

The steps for finding the factors of any number are as follows:

  • Divide the number by two to get a new one. Round the resultant number to the nearest integer if it is not an integer.
  • Divide the supplied number by each number from 1 to the resultant number (from step 1), and see which one leaves a 0. Because any number bigger than half of a particular number cannot be its factor, we only divide by these numbers.
  • The factor of that number is the divisor of each such division (with remainder 0). Furthermore, the supplied number is a factor of its own.

The following are all the factors of 120 that divide 120 without leaving a remainder:

  • 120 / 1 = 120
  • 120 / 2 = 60
  • 120 / 3 = 40
  • 120 / 4 = 30
  • 120 / 5 = 24
  • 120 / 6 = 20
  • 120 / 8 = 15
  • 120 / 10 = 12

Important Reminders

  • Any number cannot have fractions or decimals that are not integers as factors.
  • The additive inverse of a number that is a factor of the provided number is also a factor of the given number. Because 8 is a factor of 120, -8 is a factor of 120 as well.

120 factors Prime Factorisation (PF)

The number 120 is made up of several different numbers. Let’s look for the prime factors of 120.

  • To get a fraction, divide 120 by the smallest prime factor, 2, and then divide by 2 until you get a fraction.

30 / 2 = 15

60 / 2 = 30

120 / 2 = 60

7 / 2 = 3.5 so, 3.5 is not the factor.

  • Now, Continue dividing until you get a fraction or 1 with the next prime number, which is 3.

25 / 5 = 5

4 / 3 = 1.33 so, it cannot be a factor.

Let’s look at a few more examples to help you learn the idea of prime factorisation:

  • The Factors of 48 are 48,24,16,12,8,6,4,3,2,and 1
  • The factors of 54 are 54,27,18,9,6,3,2 and 1
  • The factors of 55 are 55,5,11 and 1
  • The factors of 58 are 58,29,2 and 1.
  • The factors of 256 are 256,128,64,32,16,8,4,2 and 1

Pairs in 120 Factors

By writing 120 as a product of two numbers in all feasible ways, the pair factors of 120 may be found. Both multiplicands in each product are factors of 120.

  1. A product that results in 120 – 1 × 120

Factors pair of 120 – (1, 120)

  1. A product that results in 120 – 2 × 60

Factors pair of 120 – (2, 60)

  1. A product that results in 120 – 3 × 40

Factors pair of 120 – (3, 40)

  1. A product that results in 120 – 4 × 30

Factors pair of 120 – (4, 30)

  1. A product that results in 120 – 5 × 24

Factors pair of 120 – (5, 24)

  1. A product that results in 120 – 6 × 20

Factors pair of 120 – (6, 20)

  1. A product that results in 120 – 8 × 15

Factors pair of 120 – (8, 15)

  1. A product that results in 120 – 10 × 12

Factors pair of 120 – (10, 12)

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

Helpful Hints

Keep the following in mind while determining a number’s factors:

  • A number’s factors are always 1 and the number itself.
  • To find the number’s additional components, we must first determine its prime factorisation. The prime factors of the number are therefore multiplicands of the prime factorisation.
  • The composite factors of a number are obtained by multiplying some or all multiplicands in various combinations.

Example 1: Find 120 and 121 common factors.

Solution 1:

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

The factors of 121 are 121, 11 and 1.

Therefore, the common factor of 120 and 121 is 1.

Example 2: Find  120 and 119 common factors.

Solution 2:

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

Factors of 119 = 119,17,7 and 1 

Therefore, the common factor of 120 and 119 is 1.

 Conclusion

Use the methods mentioned in this article to find the number of factors of 120. You can easily determine the results of similar factors by following the examples shown in this article.

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