Factors of 120: Method, Total Number of Factors – Mindspark.

What do we mean by Factors of 120?

The factors of a number x  are the numbers that completely divide x with zero as a remainder. It means that if y divides x and the remainder is 0 then we say that y is a factor of x.

Factors of 120 i.e, the numbers which completely divide 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Therefore 120 has a total of 16 factors.

Factors of 120 by Division Method

The easiest way to calculate the factors of any number is by first dividing the number by its smallest factor. So the number which will divide the number completely and the quotient will also be the factor( This is also known as Pair of the factors). We will repeat this process till we find all the factors.

We know that 1 will be the factor of every number, so 

\frac{120}{1}=120, therefore 1 and 120 will be the factors of 120. Now we’ll do it with numbers greater than one.

\frac{120}{2}=60

\frac{120}{3}=40

\frac{120}{4}=30

\frac{120}{5}=24

\frac{120}{6}=20

\frac{120}{8}=15

\frac{120}{10}=12

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

Factors of 120 by Tree Method

The tree method is also known as Prime Factorisation. Prime Factorisation of a number means the way of writing the numbers by using its prime factors. For example, we will write 120 as 2 ×  2 × 2 × 3 × 5.     

We call it a tree method because the number of which we have to find the factors is the highest factor of itself (highest branch), the rest of the factors are lower than the number and when we simplify it we get the prime numbers (which are one of the smallest factors of the number) and this forms a shape like a tree as we are branching out 120 into its prime factors.

120  can be written with prime factorisation as-

     120 =2^{3} \times 3 \times 5
\Rightarrow 120 =2 \times 2 \times 2 \times 3 \times 5

Factors of 120 in the form of Pairs

We can write the factors in the form of pairs. The pair means that when we will multiply the two numbers well get the result as 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

Therefore the Pairs factor of 120 are (1,120),(2,60),(3,40),(4,30),(5,24),(6,20),(8,15),(10,12).

Factors of a number can be negative too but only when they are in pairs and negative. Since, when we multiply the two negative numbers we get a positive number and in this case, the result is 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

Therefore the negative Pairs factor of 120 are (−1,−120),(−2,−60),(−3,−40),(−4,−30),(−5,−24),(−6,−20),(−8,−15),(−10,−12).

Examples 

1. Which of the following are factors of 120?

    9,10,12,15,16

Ans:

10,12 and 15 are factors of 120 as they completely divide 120. 

9 and 16 are not factors of 120 as when we divide 120 from 9 and 14 we do not get a natural number

120/9  = 13.33 

120/16= 7.5

2. Is 240 a factor of 120? 

Ans:

No, 240 is not a factor of 120. The highest factor of a number will be the number itself. 240 is a multiple of 120 as 120 x 2 = 240.

POINTS TO REMEMBER

• 1 is a factor of every number therefore it is known as a universal factor and the smallest factor of a number. 
• The highest factor of a number will be the number itself.
• A number having more than two factors is called a non-prime (composite number) number. Therefore 120 is a composite number.