CBSE Class 11-science Answered

Dear student,

The logic is as follows -

Lets say we need to find out the factors of a number N.

We prime factorize it in the form say 2^k.

(for the sake of simplicity, I have taken only one prime factor here. We can easily extend the concept to more than one prime factors.)

Now, any number of the form 2ⁱ (where i is an integer such that 0<= i <= k) is also a factor of N, as it divides 2^k which in turn divides N.

So for the values of i in set S = {0, 1, 2 , 3, 4, .... , k}, we have a factor of N. ( for i=0, 2ⁱ = 1, which is always a factor of every real number).

Since there are (k + 1) values in the set S, therefore the number of factors for N are k+1.

For your example, the value of k = 5.

i=0 , 2⁰=1 is a factor.

i=1 , 2¹=2 is a factor.

i=2 , 2²=4 is a factor.

i=3 , 2³=8 is a factor.

i=4 , 2⁴=16 is a factor.

i=5 , 2⁵=32 is a factor.

=> 5+1 = 6 factors.