Formula for Number of Factors of a number

Learn how to know the number of factors or number of divisors of any given number. Sometimes, all the factors of a number are not required to list. Only the number of factors we need to find out. In that case this formula will be very helpful.

The meaning of factor or divisor is, it is a number which divides the given number exactly. Now we learnt what is a factor, after this we will see how many such factors will be there for any given number. All the numbers will be having some number of factors. We know that based on the number of factors, we are defining what are prime numbers and what are composite numbers. So it is very much required to know no. of factors of a number. This you can know it by the formula.

Number of factors formula as follows:

Whatever may be the given number, first do prime factorization for that number. After that, write the given number as the product of the prime numbers. For example, if a number “d” is written as ${ a }^{ x }$. ${ b }^{ y }$.${ c }^{ z }$ then the number of factors of the number “d” is given by product of (x+1), (y+1) and (z+1).

Examples:

The number 8 is written as ${ 2 }^{ 3 }$. So the number of factors of 8 = (3+1) = 4

20 is written as ${ 2 }^{ 2 }$.${ 5 }^{ 1 }$, No. Of factors of 20 = (2+1). (1+1) = 3.2 = 6

42 is written as ${ 7 }^{ 1 }$.${ 2 }^{ 1 }$.${ 3 }^{ 1 }$ = (1+1).(1+1) .(1+1) = 2.2.2 = 8

The number 100 is written as ${ 5 }^{ 2 }$.${ 2 }^{ 2 }$, so the no. of factors of 100 = (2+1).(2+1) = 3.3 = 9

256 is written as ${ 2 }^{ 8 }$, therefore the no. of factors of 256 = (8+1) = 9

78 is written as ${ 2 }^{ 1 }$.${ 3 }^{ 1 }$.${ 13 }^{ 1 }$, therefore the no. of factors of 78 = (1+1).(1+1).(1+1)= 2.2.2 = 8