Prime Factorization Using the Ladder Method

The ladder diagram method presents a structured approach to breaking down numbers into their prime factors. This systematic process involves dividing numbers by prime factors until reaching the smallest possible prime numbers.

Definition: Prime factorization is the process of breaking down a number into a product of prime numbers.

Example: The number 36 is broken down through the following steps:

1. 36 ÷ 2 = 18
2. 18 ÷ 2 = 9
3. 9 ÷ 3 = 3
4. 3 ÷ 3 = 1

Highlight: The final result can be written in two forms:

• Expanded form: 2 × 2 × 3 × 3
• Exponential form: 2² × 3²

Vocabulary:

• Prime number: A number that has exactly two factors - 1 and itself
• Exponential form: A way to write repeated multiplication using powers
• Expanded form: Writing out all prime factors as multiplication

Quote: "Pick a prime number and divide, repeat until all prime factors are found."