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# 6th Grade - Prime Factorization

## Introduction

• A prime number is greater than 1 and has just two factors, itself and the number 1.
• A prime number can only be divided by itself and 1.
• Here is a list of prime numbers from 1-100:  2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
• Prime factorization is finding the prime numbers that multiply to make the original or given number. It is the process of breaking down numbers (through division) to find all the prime factors of the number.
• To find the prime factorization of a given number, keep dividing the given number by the smallest possible prime factor until you get to the number that cannot be further divided. The list of the factors obtained will be the prime factorization of a given number.

## Solved Examples

Example 1: Find the prime factorization of 56.

Solution:

Example 2:  Find the prime factorization of 81.

Solution: $3×3×3×3$

Example 3: Find the smallest prime factor of 36.

Solution: $2×3×2×3$

Above is the list of all the prime factors of 36, and the smallest prime factor is 2.

## Cheat Sheet

• To find the prime factorization of a number, keep dividing it by its factors until you get to the number that cannot be further divided. The list of the factors will be the prime factorization of the number.
• 2 is the only even prime number. All the other prime numbers are odd.

## Blunder Area

• 1 is neither a prime nor a composite number.
• 0 is neither a prime nor a composite number.