Prime Factorization

Before we start to find the Prime Factorization for a number, we should review what prime numbers are.

Prime Numbers

A prime number has exactly 2 factors: 1 and itself; for example, 11 is a prime number because the only numbers that divide equally into it are 1 and 11.

Composite Numbers

Composite numbers have more than 2 factors, for example, 4 is a composite number because 1, 2, and 4 can divide into it without having a remainder.

One

One is not considered to be prime or composite since it has exactly 1 factor.

After a quick review of what factors are, we look at how to make factor trees to find all the prime factors.

Prime Factorization:

 

Remember:

When you are finding the prime factors of a number, you are finding the prime numbers, that when multiplied together, equal the original number.
 
For example: Prime factorization of 72
$72=2*2*2*3*3$
      $=2^3*3^2$
 
 
To explore “The Sieve of Eratosthenes,” a method for finding prime numbers check out “Did you Know”
To see a connection between the Fibonacci Sequence and Prime numbers (or to read about other patterns) check out “Hey! This might be fun to look at next.”


Hey!

This might be be fun to look at next: