Prime Factorization

Number Theory

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.

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: $72=2*2*2*3*3$
$=2^3*3^2$

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!

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