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

## Leave a Reply