Prime Factorization

PRIME FACTORIZATION
This page is just a rough draft.

Prime and Composite Numbers
Prime Number: A whole number greater than 1 whose only factors are 1 and itself.
Composite Number: A whole number greater than 1 and has more than two whole number factors.

Factors

Activity
Write down a multiplication problem.
Label the factors. Label the product.

Example:
3 x 2 = 6
/      \     \
factors   product

Factors: A number that is multiplied by another number to find a product.
Product: The answer to a multiplication problem.

1.3 6th Grade Big Ideas Math

PRIME FACTORIZATION

Find all the factors of a number.
List the factor pairs of that number.

Examples:

6
Factors of 6:
1 x 6 or 6 x 1
2 x 3 or 3 x 2

Factors of 6:
1, 2, 3, 6

Factor Pairs of 6:
1, 6 or 6, 1
2, 3 or 3, 2

18
1 x 18 or 18 x 1
2 x 9 or 9 x 2
3 x 6 or 6 x 3

Factors of 18:
1, 2, 3, 6, 9, 18

Factor Pairs of 18:
1, 18 or 18, 1
2, 9 or 9, 2
3, 6 or 6, 3

Activity
Write examples like the above examples in your interactive notebook.

Prime Factorization
Terms:
Prime Factors: These are prime numbers that divides into a number exactly.
Prime Factorization: Is a number that is written as the product of all its prime factors.
The prime factorization of a composite number is the number written as a product of its prime factors.

Examples:
So, if we want to find all the factors of _____, we just want to list all the ways we can get _____ using whole numbers and multiplying.

Let’s look at the number 18 again. Let’s find the prime factorization of this number. We can use a factor tree.
We write the prime factorization by factoring until only prime factors are in the product.
We start with two factors of 18. This can be any two factors of 18. Let’s start with _____ 2 X 9. What are two other factors that could be used? (3 X 6)

Factor Tree

    18
   /   \
  2    9
      /  \
     3    3

Step 1: Write down the number you are trying to find the prime factorization.
Step 2: 2 X 9
Step 3: 2 is a prime. 9 is a composite number.
Step 4: We can factor 9 as 3 X 3.
Step 5: Now all the numbers are primes, 2 x 3 x 3
Step 6: Writing the prime factorization using exponents, we have 2 X 3^2.
The prime factorization of 18 is 2 X 3^2.    
Check: 2 X 3^2      2 x 9 = 18
18 = 2 X 3^2

Activity:
Pick a number. Find the prime factorization for that number using a factor tree.

Example:
         72
        /   \
       8    9
     /  \  /  \
    2   4 3   3
       /  \
      2   2

The prime factorization of 72 is 2^3 x 3^2.

Prime Numbers and Composite Number
Activity: Foldable