**Prime & Composite Numbers:**(1)

__Prime Number:__A number larger than 1, that can only be evenly divided by the numbers 1 and itself OR a number larger than 1, whose only factors are 1 and itself.

Examples:

- 37 is a prime number. The only factors of 37 are: 1, 37
- 11 is a prime number. The only factors of 11 are: 1, 11

__Composite Number__: A number larger than 1 that can be evenly divided by numbers other than 1 and itself or a number larger than one who has more than two factors

- 63 is a composite number. The factors of 63 are: 1, 3, 7, 9, 21, 63
- 40 is a composite number. The factors of 40 are: 1, 2, 5, 8, 20, 40

**Finding the Greatest Common Factor, GCF**-When asked to find the greatest common factor of two or more numbers you are looking for the

**BIGGEST**factor that two or more numbers share.

-Factors break numbers down evenly.

-A number’s factors will always be

**LESS THAN**or

**EQUAL**to the given number.

__Example:__

Find the factors of 16:

16: 1 x 16, 2 x 8, and 4 x 4

- If you look at the factors of 16 you see that 16 is the biggest factor (16 = 16), and then ALL of the other factors are smaller than 16.

__Example:__

Find the GCF of 32 & 48:

(1) List the factors

32: 1, 2, 4, 8, 16, 32

48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

(2) Identify the factors that they have in common: 1, 2, 4, 16

(3) Identify the LARGEST or GREATEST factor that they have in common: 16

GCF = 16

When identifying the factors of a given number you may use:

(1) Factor Rainbow

(2) Listing Factor Pairs

(3) Venn Diagram

(4) L Method

The Rainbow Method L Method

**Finding the Least Common Multiple, LCM**-A number’s multiples will always be

**GREATER THAN**or

**EQUAL**to the given number.

-Multiples are the products you find when you multiply a given number by other numbers.

__Example:__

Find the first six multiples of 8:

8: 8, 16, 24, 32, 40, 48

- If you look at the multiples of 8 you see that 8 is the smallest multiple (8 = 8), and then ALL of the other multiples are larger than 8.

__Example:__

Find the LCM of 6 & 10:

(1) List the multiples of each number

6: 6, 12, 18, 24, 30, 36, 42, 48, 54...

10: 10, 20, 30, 40, 50, 60...

(2) Identify the smallest multiple that they share, or have in common

6: 6, 12, 18, 24, 30, 36, 42, 48, 54...

10: 10, 20, 30, 40, 50, 60...

The LCM of 6 and 10 is 30.

When finding the LCM of two or more whole numbers you may...

(1) List the multiples (shown above)

(2) Create a table

(3) Use the "L" Method

**Create a table L Method**

__Differing between GCF and LCM Word Problems__

If you're struggling with GCF try watching this video: How to find the GCF of two or more whole numbers.

GCF Practice Game

LCM Word Problem:

__Differing between GCF and LCM Word Problems__

**GCF Word Problem:**

**Prime Factorization**In order to find the prime factorization of a given whole number, you must continue to break down the given whole number into factor pairs until you are left with a string of prime factors.

You can use a

**factor tree**:

You can also determine the prime factorization of a given whole number using the

**birthday cake method****You can use the prime factorization to find the GCF of two or more whole numbers: Try watching this**video

**Order of Operations**The order of operations is the sequential order in which you should complete operations within a numerical expression when more than 1 operation is present.

__Distributive Property__In order to create an equivalent expression according to the distributive property, you must multiply the outside numbers by BOTH numbers inside the parentheses.

If possible you may then add the two products.

You will get the same answer as you would if you evaluated the expression according to the order of operations.

You will get the same answer as you would if you evaluated the expression according to the order of operations.

In order to factor an expression according to the distributive property, you must identify the GCF of the two whole numbers in the expression.

Then divide the two whole numbers by the GCF.

Write the quotient inside the parentheses.

Then divide the two whole numbers by the GCF.

Write the quotient inside the parentheses.