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OUR LESSON

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Warm Up

1) 139

Determine whether each number is prime or composite

Prime

2) 1700 Composite

3) 17 Prime

4) 333 Composite

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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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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

Review

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Lets take an Example

280

2 140

2 70 2 35

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

Factor Tree of 280

7 and 5 are Prime numbers so cannot be factored further

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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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List the factors of each number. Then identify the common factors. The greatest of these common factors is the GCF

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

Find the GCF of 27 and 36

List all the factors of both the numbers

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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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Write the prime factorization

27 36

3 x 9 3 x 12

3 3 x 3 3 x 4 3 3 2 x 2

Factor Tree method

Lets take the same example to find the factors of 27 and 36

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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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Method 2

Write the prime factorization

The common prime factors are 3 and 7 so the GCF is

3 x 7 = 21

Finding GCF of 63 and 42

63 = 3 x 3 x 7

42 = 3 x 2 x 7

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Find the prime factorization of 45a2b3

45a2b3 = 9 • 5 • a • a • b • b • b

= 3 • 3 • 5 • a • a • b • b • b

= 32 • 5 • a • a • b • b • b

Write the variables without exponents

Lets see another Example

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Now you try some

Find GCF of the following numbers

1) Find the GCF of 40a2b and 48ab4 8ab

2) 160 and 550 10

3) 20a2 and 14ab 2a

4) 36, 24, 144, 96 12

5) 15, 25 and 30 5

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6) The GCF of any two numbers is highest of their common factors

Find the GCF of each pair of numbers by listing their common prime factors

7) 80 and 110 common prime factors : 2, 5 and GCF : 10

8) 42 and 49 common prime factors: 7 and GCF : 7

9) Name a pair of numbers whose GCF is 1 14, 33

10) What is the GCF of all numbers in the sequence 12,

24, 36, 48,….? 12

Questions

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Break Time

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It's GAME TIME !!!!

Click here to play a game

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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?

48 = 2 x 2 x 2 x 2 x 354 = 2 x 3 x 3 x 3GCF = 2 x 3

= 6

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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.

Find the GCF of 8, 64, 968: 2 x 2 x 2

64: 2 x 2 x 2 x 2 x 2 x 2

96: 2 x 2 x 2 x 2 x 2 x 3

The GCF is 2 x 2 x 2 = 8 Thus there will be 8 crayons in each row

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3) Can the GCF of a set of numbers equal to one of the numbers itself? Explain

Yes for the set 2 and 4 The GCF is 2

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Let us review what we have 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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List the factors of each number. Then identify the common factors. The greatest of these common factors is the GCF

Method 1

Write the prime factorization of each number. Then identify all common prime factors and find their product, to get the GCF

Method 2

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Find the GCF of these set of numbers

66 and 72a) b) 10, 20, 35

GCF 6 GCF 5

c) 9, 11

GCF 1

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Great Job Done

Be sure to practice what you have learned today