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 2k.
(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 2k 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.