Question

If you write 14 to the 6 power in expanded form, how many factor will there be?

Answer 1

14 to the 6th power is 7,529,536. There are zero factors.

Answer 2

49

Explanation:

The expanded form of 14 to the power 6 can be written as follows

`14^(6)= 2^(6)* 7^6`

since 2 and 7 are prime numbers hence they can not be broken down into smaller factors.

now according the rule of finding factors

total number of factor= (a+1)*(b+1)

where a and b are powers of the prime factors

therefore, total number of factor= (6+1)*(6+1)= 7*7= 49