1. GREATEST COMMON FACTOR
Good Afternoon!
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Warm Up
Determine whether each number is prime or composite
1) 139
2) 1700
3) 17
4) 333
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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.
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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
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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
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6. 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
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7. 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
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Method 2
Write the prime factorization of each number.
Then identify all common prime factors
Multiply these numbers
Their product is the GCF
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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
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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
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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
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12. 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.
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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
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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,….?
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Break Time
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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?
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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.
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3) Can the GCF of a set of numbers equal to one of the numbers itself? Explain
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20. 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
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Method 1
List the factors of each number. Then identify
the common factors.
The greatest of these common factors is the
GCF
Method 2
Write the prime factorization of each number.
Then identify all common prime factors and find their
product, to get the GCF
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22. Great Job! Remember to practice what you have learned today
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