Lesson 2 - Prime Factorization

• Write a given number as a product of its prime factors

What is a prime factor?

What is the meaning of prime factorization?

How do you express a number as a product of its prime factors?

How can understanding factors help you understand the world around you.

Prime numbers - have exactly two factors and these factors are 1 and the number itself. Thus, 2, 3, 5, 7, 11, and 13 are prime numbers.

Numbers that have more than two factors are composite. Also, a composite number can be written as a product of two numbers, neither of which is 1 nor itself.

Example: 

Eighteen has more than two factors: 1, 2, 3, 6, 9, and 18.

Eighteen can be written as 1 × 18, 3 × 6, or 2 × 9. 

Therefore, 18 is a composite number.

What is the only prime number that is even?

Is 57 a prime number? Why or why not?

One has only 1 factor, which is 1. It is neither prime nor composite. Only counting numbers greater than 1 may be classified as prime or composite.

Here are the prime factorizations of 18, 24, and 30:

18 = 2 × 3 × 3 24 = 2 × 2 × 2 × 3 30 = 2 × 3 × 5

Notice that the factors or numbers we multiply are all prime. The prime factorization of a number is the product of prime factors. To find prime factors of a number, start with 2, and use it as a factor as many times as possible. Next, try 3, then 5, and so on. Continue dividing until you have found all the prime factors of the number.

A centered dot (•) is used as a symbol for multiplication. Hence, you can also write

2 × 3 × 5 as 2 • 3 • 5 and 2 × 3 × 7 as 2 • 3 • 7.

You can get the prime factorization of any composite number by using a factor tree or by

continuous division using the prime factors of the number as divisors.

Practice

Complete the prime factorization of each composite number.

1. 50 = 2 × ___ × 5

2. 81 = 3 × 3 × ___ × 3

3. 48 = 2 × ___ × 2 × ___x 3

4. 27 = 3 × 3 x___

5. 54 = 2 × ___ × 3 × 3

Keep Practicing

Write the composite number for each prime factorization.

1. 3^2• 5 • 7 = _______ 4. 27 = 3 × 3 x___

2. 2 • 5^2• 11 = _______       5. 54 = 2 × ___ × 3 × 3

3. 48 = 2 × ___ × 2 × ___x 3