1. How can I write numbers in different ways?
4.3 Prime Factorization
How can I write numbers in different ways?

2. Vocabulary – Please copy the following into your notebook:
prime number – a whole number that has exactly two factors, 1 and itself
composite number – a whole number that has more than two factors

3. Please copy the following two examples into your notebook.
Let’s determine if the following numbers are prime or composite: 19
Find the factors of 19 by listing the whole number pairs whose product is 19.
19 = 1 (19)
The number 19 has only two factors. Therefore, 19 is a prime number.

4. 28
Find the factors of 28 by listing the whole number pairs whose product is 28.
28 = 1(28)
28 = 2(14)
28 = 4(7)
The factors of 28 are 1,2,4,7, and 28. Since the number has more than two factors, it is composite.

5. Now, you try!
First, list the factors of the following numbers. Second, determine whether the number is prime or composite. 36 The factors of 36 are 1,2,3,4,6,9,12,18, and is composite. 31 The factors of 31 are 1 and is prime. If you are confused, please ask someone in your group for help. If you have asked everyone in your group, please ask Mrs. McLead for help.

6. More Vocabulary – Please copy the following into your notebook:
prime factorization– a composite number expressed as the product of prime factors
factor tree – one way to find the prime factorization of a number

7. Please copy the following example into your notebook.
Please find the prime factorization of 24 using a factor tree. 24
Write the number that you are factoring at the top of your factor tree. 12 2
Because 3 is a prime number, we will circle it.
Continue to factor numbers that are not prime.
Choose any pair of whole number factors of 24.
Because 2 is a prime number, we will circle it. 3 4
Continue to factor numbers that are not prime. 2 2
Because 2 is a prime number, we will circle both 2s.
Now, we will look at the circled numbers to determine the prime factorization.
We write the smallest numbers first, so the prime factorization of 24 is 2·2·2·3, or 23·3

8. Now, you try!
Please find the prime factorization of 36. Click when you think you have the answer.
The prime factorization of 36 is 2·2 ·3 ·3, or 22·32.

9. The LAST vocabulary of the day
To factor – to write a number as a product of its factors. A monomial can be factored as a product of prime numbers variables with no exponents greater than 1. Negative coefficients can be factored using -1 as a factor.

10. Please copy the following example into your notebook.
Please factor the following monomial:
First, we will find the prime factors of 8.
The prime factors of 8 are 2, 2, and 2. We will write the monomial as:
2·2 ·2 ·a ·b ·b 8 2 4 2 2

11. Please go to:
and the results to