factors

For the number 6¹⁰ x 7¹⁷ x 55²⁷, find

1.       The number of prime factors

2.       The number of all the factors.

Answer:

Rewriting the expression in terms of prime numbers, we get

6¹⁰ x 7¹⁷ x 55²⁷ = 2¹⁰ x 3¹⁰ x 7¹⁷ x 5²⁷ x 11²⁷

1.       Total number of prime factors = sum total of all the indices = 10 + 10 + 17 + 27 + 27 = 91

2.       Total number of factors = (10 + 1)(10 + 1)(17 + 1)(27 + 1)(27 + 1) 

= 11x11x18x28x28 = 1707552