Question

160) Find all the prime factors of (3^18 - 2^18)

Answer 1

To answer this question we will construct the factor tree.

Computing the subtraction we get:

`3^(18)-2^(18)=387158345.`

Dividing the above result by 5 we get:

`(387158345)/(5)=77431669.`

Dividing by 7 we get:

`(77431669)/(7)=11061667.`

Dividing by 19 we get:

`(11061667)/(19)=582193.`

Dividing by 577 we get:

`(582193)/(577)=1009.`

Notice that 1009 is a prime number.

Therefore the factor tree is as follows:

Answer: The prime factors of (3^18 - 2^18) are 5, 7, 19, 577, and 1009.