Download 2-4 GCF

Unit A: Expressions and Equations
Name: ____________________________________ Date: ____________________ Class Period: _____
LESSON 2-4: GREATEST COMMON FACTOR
Example 1: Finding the Greatest Common Factors
What is the greatest common factor (GCF) of 36 and 54?
Step 1: List the factors of 36 and 54
Factors of 36:
Factors of 54:
Step 2: Circle and list the common factors. _________________________________________
Step 3: The GREATEST common factor of 36 and 54 is: ________________
Key Concept:
Vocabulary Word
Factor
Definition
A factor is a number that divides another number without a
______________.
Common Factor
A common factor is a factor that two or more numbers
___________________.
Greatest Common
Factor
The greatest common factor of two or more whole numbers is the
greatest number that is a ____________ of all the numbers. You can
refer to the greatest common factor as the GCF.
Key Concept:
Vocabulary Word
Definition
Prime Number
A prime number is a whole number
greater than 1 with exactly _________
factors, 1 and itself.
Composite Number
A composite number is a whole
number greater than 1 with _________
than two factors.
Example
Unit A: Expressions and Equations
Prime Factorization: The expression of a composite number as a product of prime factors.
You can use a prime factorization tree to find the prime factorization of a number.
For example:
1. Write any 2 factors of 30.
2. If 1 of the numbers is prime, circle it.
3. Now draw 2 new branches with factors.
4. Circle any numbers that are prime.
5. Continue in this way until all of the braches end in a circled number.
Example 2: Finding Prime Factorization of Numbers
Find the prime factorization of 72. Use a factor tree.
Example 3: Using Prime Factorization to Find GCF
Find the GCF of 84 and 63 using a factor tree.
Another method to find the Prime factorization of Number is using Euclid’s Ladder
to find the GCF of 42 and 28
Step 1: Put the two numbers that you
want to find the GCF of at the top
of the ladder
Step 2: Think of the smallest prime
number that can divide into BOTH
numbers. Divide.
Step 3: Repeat Step 2 until there is
nothing left to divide by other
than 1.
Step 4: Multiply the numbers on the side
of the ladder. This will be the
GCF of the two numbers.