## 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: $2\times 2\times 2\times 7$

__Example 2: __ Find the prime factorization of 81.

Solution: $3\times 3\times 3\times 3$

__Example 3__: Find the **smallest prime factor** of 36.

Solution: $2\times 3\times 2\times 3$

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.

- Rishi Jethwa
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