Prime Factorization Lesson: Definitions and Methods

Lesson Overview

• What Is Prime Factorization?
• How to Find Prime Factors
• Prime Factorization Solved Examples

Prime factorization is a way to express any whole number as a product of prime numbers. This process is important for simplifying fractions, finding the greatest common factor, and solving problems.

What Is Prime Factorization?

Prime factorization is the process of expressing a composite number as a product of its prime factors. A prime number is a whole number greater than 1, divisible only by 1 and itself.

Examples:

• 12 = 2 x 2 x 3
• 36 = 2 x 2 x 3 x 3
• 105 = 3 x 5 x 7

Take this quiz -

5th Grade Math Quiz on Prime Factorization! Trivia Questions

How to Find Prime Factors

Prime factors can be determined using various methods, including the division method and the factor tree method. Both methods involve iterative division by prime numbers to arrive at the prime factorization of a composite number.

Prime Factorization Methods

Division Method

This method uses repeated division by prime numbers to find the prime factors.

Example: Find the prime factors of 60.

1. Divide 60 by the smallest prime number, 2: 60 ÷ 2 = 30

1. Divide 30 by 2 again: 30 ÷ 2 = 15

1. 15 is not divisible by 2, so divide by the next prime number, 3: 15 ÷ 3 = 5

5. 5 is a prime number.

Therefore, the prime factorization of 60 is 2 x 2 x 3 x 5.

Factor Tree Method

This method visually represents the prime factorization as a tree with branches.

Example: Find the prime factors of 60.

1. Start with 60 at the top.
   
2. Branch down to two factors of 60, such as 2 and 30.
   

Continue branching down for each composite factor until you reach prime numbers.

60 /
2 30 /
2 15 /
3 5

Therefore, the prime factorization of 60 is 2 x 2 x 3 x 5.

Prime Factorization Solved Examples

1. Find the prime factorization of 48.

Using the division method:

Divide 48 by 2: 48 ÷ 2 = 24 Divide 24 by 2: 24 ÷ 2 = 12 Divide 12 by 2: 12 ÷ 2 = 6 Divide 6 by 2: 6 ÷ 2 = 3 3 is a prime number.

Therefore, the prime factorization of 48 is 2 x 2 x 2 x 2 x 3.

2. Find the prime factorization of 75.

Using the factor tree method:

Start with 75 at the top of the tree. Branch down to two factors of 75, such as 3 and 25. Branch down 25 to 5 and 5.

75 /
3 25 /
5 5

Therefore, the prime factorization of 75 is 3 x 5 x 5.

3. Find the prime factorization of 126.

Using the division method:

Divide 126 by 2: 126 ÷ 2 = 63 63 is not divisible by 2, so divide by the next prime number, 3: 63 ÷ 3 = 21 Divide 21 by 3: 21 ÷ 3 = 7 7 is a prime number.

Therefore, the prime factorization of 126 is 2 x 3 x 3 x 7.

4. Find the prime factorization of 200.

Using the factor tree method:

Start with 200 at the top of the tree. Branch down to two factors of 200, such as 2 and 100. Branch down 100 to 10 and 10. Branch down each 10 to 2 and 5.

200 /
2 100 /
10 10 / \ /
2 5 2 5

Therefore, the prime factorization of 200 is 2 x 2 x 2 x 5 x 5.

5. Find the prime factorization of 315.

Using the division method:

315 is not divisible by 2. Divide 315 by 3: 315 ÷ 3 = 105 Divide 105 by 3: 105 ÷ 3 = 35 35 is not divisible by 3, so divide by the next prime number, 5: 35 ÷ 5 = 7 7 is a prime number.

Therefore, the prime factorization of 315 is 3 x 3 x 5 x 7.

Take These Quizzes -

Prime Factors Quiz: Trivia Test!

Take The Prime Factorization Math Test!