# GREATEST COMMON FACTOR

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GREATEST COMMON FACTOR
Good Afternoon! Copyright © Ed2Net Learning, Inc.

Warm Up Determine whether each number is prime or composite 1) 139 2) 1700 3) 17 4) 333 Copyright © Ed2Net Learning, Inc.

Lets review what we have learned in the last lesson When a whole number, greater than one has only 2 factors, 1 and whatever your number is, it is called a Prime Number. When a whole number greater than one has more than 2 factors it is called a Composite Number The numbers 0 and 1 are neither Prime or Composite. Copyright © Ed2Net Learning, Inc.

Review The number 60 is a composite number. It can be written as the product 2 x 2 x 3 x 5. 2, 3 and 5 are factors of 60 and all these factors are prime numbers. We call them prime factors. When we express a number as a product of prime factors, we have actually factored it completely. We refer to this process as prime factorization Copyright © Ed2Net Learning, Inc.

Lets take an Example Factor Tree of 280 280 7 5 So, the Prime Factorization of 280 expressed as a product of Factors looks like this … 2 x 2 x 2 x 7 x 5 Simplified to: 23 x 7 x 5 7 and 5 are Prime numbers so cannot be factored further Copyright © Ed2Net Learning, Inc.

Two methods can be used to find GCF
Lets Get Started! Greatest Common Factor (GCF) of two or more numbers is the greatest number that is a factor of each number Two methods can be used to find GCF Copyright © Ed2Net Learning, Inc.

Method 1 List the factors of each number. Then
identify the common factors. The greatest of these common factors is the GCF Find the GCF of 27 and 36 List all the factors of both the numbers Factors of 27 : 1, 3, 9, 27 Factors of 36 : 1, 2, 3, 4, 6, 9, 12, 18, 36 Common factors 1, 3, 9 Thus, the GCF of 27 and 36 is 9 Copyright © Ed2Net Learning, Inc.

Method 2 Write the prime factorization of each number. Then identify all common prime factors Multiply these numbers Their product is the GCF Copyright © Ed2Net Learning, Inc.

Lets take the same example to find the factors of 27 and 36 Write the prime factorization 3 x x x x 4 3 x 2 Factor Tree method 27 = 33 36 = 32 x 22 The GCF of 27 and 36 is 32 = 9 Copyright © Ed2Net Learning, Inc.

Lets take another example Find the GCF of 63 and 42 Method 1 List the factors 63: 1, 3, 7, 9, 21, 63 42: 1, 2, 3, 6, 7, 14, 21, 42 Since the common factors are 1, 3, 7 and 21; the GCF is 21 Copyright © Ed2Net Learning, Inc.

Finding GCF of 63 and 42 Method 2 Write the prime factorization = x x 42 = x x The common prime factors are 3 and 7 so the GCF is 3 x 7 = 21 Copyright © Ed2Net Learning, Inc.

Lets see another Example
Find the GCF of 6a3b and 4a2b 6a3b = 2 x 3 x a3 x b 4a2b = 2 x 2 x a2 x b GCF = 2 x a2 x b = 2a2b Write the prime factorizations Find the common factors. Use the lesser power of the common factors. Copyright © Ed2Net Learning, Inc.

Now you try some Find GCF of the following numbers 1) Find the GCF of 40a2b and 48ab4 2) and 550 3) 20a2 and 14ab 36, 24, 144, 96 15, 25 and 30 Copyright © Ed2Net Learning, Inc.

Questions The GCF of any two numbers is ______of their common factors Find the GCF of each pair of numbers by listing their common prime factors 7) 80 and 110 42 and 49 9) Name a pair of numbers whose GCF is 1 10) What is the GCF of all numbers in the sequence 12, 24, 36, 48,….? Copyright © Ed2Net Learning, Inc.

Break Time Copyright © Ed2Net Learning, Inc.

1) The school band has 54 members while the choir has 48 members. What is the greatest number of rows that each group and be broken into if the number of rows are the same for the two groups? Copyright © Ed2Net Learning, Inc.

2) What would be the greatest number of crayons in each row of an 8 64 and a 96 crayon box, if all rows have the same number. Copyright © Ed2Net Learning, Inc.

3) Can the GCF of a set of numbers equal to one of the numbers itself? Explain Copyright © Ed2Net Learning, Inc.

Let us review what we have We can find the GCF by using 2 methods
learnt today Greatest Common Factor of two or more numbers can be defined as the greatest number that is a factor of each number We can find the GCF by using 2 methods Copyright © Ed2Net Learning, Inc.