tutorial on number of factors

To find the number of factors of a number

If a number N can be expressed as product of prime factors such that

N = p^a x q^b x r^c...............................

Then, the total number of factors including N and 1 is given by

(a + 1)x(b + 1)x(c + 1).................................

Example:

Find the total number of factors of 222.

222 = 2 x 3 x 37

Or, 222 = 2¹ x 3¹ x 37¹

So, the total number of factors = (1+1)x(1+1)x(1+1) = 2x2x2 = 8

We can check the answer as shown below.

The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222.

Find the total number of factors of 64.

64 = 2⁶

So, the total number of factors = (6+1) = 7

We can check the answer as shown below.

The factors of 64 are 1, 2, 4, 8, 16, 32, 64.