Answer:
The prime factorization of the number 256;
The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
or also written as { 2, 2, 2, 2, 2, 2, 2, 2 }
So written in exponential form is: 2 ^8
To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.
Why is it written as 2 ^8?
Let's start by dividing 256 by 2
256 ÷ 2 = 128
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
The "BOLD" divisor(s) above are the prime factors of the number 256. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256. It can also be written in exponential form as 28.
