Question

Find the number of factors of 120.

Answer 1

Hint: To solve this particular type of question we first need to find the prime factors of 120 and then further we need to use the formula of Total number of factors of N = (a+1)(b+1)(c+1) , where a , b , c are the powers of the prime factors of 120.



Complete step-by-step answer:
120 is a composite number so it has more than two factors unlike a prime number which has only two factors i.e ,1 and the number itself.

But 120 can be expressed in terms of its prime factors
as 120 = $2 \times 2 \times 2 \times 3 \times 5$

Other than the above 5 prime factors it has other factors too ,
The same can be calculated by

Numbers of factors = Each prime factor's highest power multiplied by each of the other factors' highest power +1.

$ \Rightarrow $N = (a+1)(b+1)(c+1) , where a , b , c are the powers of the prime factors of 120
So , here the highest power of 2 , 3 and 5 is '3' ,'1' and '1' respectively.

Therefore , 120 = (1$ \times $3+1) $ \times $ (1$ \times $1+1) $ \times $ (1$ \times $1+1) = 16 factors

Note-
Remember that factors of 120 are all the numbers which divide 120 without leaving any remainder . We can also find these numbers manually by checking all divisors of 120 and putting them in order .