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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.