tutorials -sum of factors

Sum of Factors

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

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

Write the power of each of the prime factors beginning with zero and going to thee highest power of the prime number.

Record the same for each prime number.

An example will help

64= 2⁶

Then the sum of factors (2⁰ + 2¹ + 2² + 2³ + 2⁴ + 2⁵ + 2⁶) = 1 + 2 + 4 + 8 + 16 + 32 + 64 =  127

Another Example:

Find the total number of factors of 222.

222 = 2 x 3 x 37

Or, 222 = 2¹ x 3¹ x 37¹

then the sum of factors are (2⁰ + 2¹) (3⁰ + 3¹) (37⁰ + 37¹) = (1+2)(1+3)(1+37) = 3 x 4 x 38 = 456

We will check the answer

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

Sum of factors = 456