Prime Factorization

Prime factorization refers to expressing an integer as a product of prime numbers.

What is a prime number?

• DefinitionAn integer greater than 1 that is divisible only by 1 and itself.
• Examples2, 3, 5, 7, 11, 13, etc.
• PointsA special number that is "divisible by only a few numbers (only two)."

What is a prime factor?

• DefinitionA prime number that can divide a certain number.
• ExampleThe prime factors of the number 12 are 2 and 3 (12 is 2 x 2 x 3).
• ExampleThe prime factors of the number 18 are 2 and 3 (18 is 2 x 3 x 3).
• Point Prime factors are the "parts of prime numbers" that make up a "specific number."

What is prime factorization?

• Definition Expressing a number as a product of prime numbers.
• Example When 12 is factorized, 12 = 2×2×3.
• Example When 18 is factorized, 18 = 2×3×3.
• Point It is the process or calculation of finding the "combination of prime numbers that make up that number."

1. Check the number

First, decide the number you want to prime factorize.

Example: 24

2. Divide by the smallest prime number "2"

If the number is divisible by 2, first divide it by 2. Continue until it is no longer divisible.

Example

24 ÷ 2 = 12

12 ÷ 2 = 6

6 ÷ 2 = 3 (stop because it is no longer divisible)

The prime factors obtained here are 2, 2, 2.

3. Divide by the next prime numbers "3", "5", "7", etc.

Check whether the remaining number (3 in this case) is prime.

3 is a prime number, so that's it.

4. Summarize the results

Express the results of the prime factorization in the form of a product.

Example

24 = 2 × 2 × 2 × 3

Example: Factoring "36"

36 ÷ 2 = 18

18 ÷ 2 = 9 (2 is the end)

9 ÷ 3 = 3

3 ÷ 3 = 1 (the end)

Result: 36 = 2 × 2 × 3 × 3