Welcome to Math 6

Today’s subject is…

Prime and Composite Numbers

The Connector…

This is the Golden Gate Bridge, which is in California, USA.

Until 1964, this was the longest bridge in the world. (Now its not even in the top ten.)

These are the 3 Longest Bridges in the World

Bridge NameLength

(meters)

Location

Weihe Grand Bridge 79,732 China

Bang Na Expressway 54,000 Thailand

Lake Pontchartrain Causeway

38,442 USA

On which of the bridges in the table could a light fixture be placed every 6 meters so that the first light is at the beginning of the bridge, and the last light is at the end of the bridge?

This is a divisibility question.

Lets look at the question again and interpret it…

On which of the bridges … could a

light fixture be placed every 6 meters

so that the first light is at the beginning

of the bridge and the last light is at the

end of the bridge? (No remainder)

We need to decide which of these numbers is divisible by 6.

Weihe Grand Bridge 79,732 m

Bang Na Expressway 54,000 m

Lake Pontchartrain Causeway

38,442 m

Weihe Grand Bridge: 79,732 m

To be divisible by 6, it must be divisible by 2 and 3 . Since it ends in a 2,it is

divisible by 2. Add the digits. 7+9+7+3+2=28.

x Since 28 is not divisible by 3,

it is not divisible by 6.

Bang Na Expressway 54,000 m

Since it ends with a zero, it is divisible by 2.

To check for divisibility by 3, add the digits. 5+4+0+0+0=9. The sum, 9, is divisible by 3.

54,000 is divisible by 6, since it is divisible by both 2 and 3.

Lake Pontchartrain Causeway

38,442 m

It is divisible by 2 since it has a 2 in the ones place.

Next add the digits:3+8+4+4+2=21 The sum, 21, is divisible by 3. So 38,442 is divisible by 3 too.

38,442 is divisible by 6 since it is divisible by both 2 and 3.

Divisibility Rules

2 if the last digit is 0,2,4,6 or 8

3 if the sum of the digits is divisible by 3

5 if it has a 0 or 5 in the ones place

6 if it is divisible by both 2 and 3

9 if the sum of the digits is a number that is divisible by 9

Factor - A number that is multiplied by another number to get a product.

When we say 60 is ‘divisible’ by 10, we can also say that 10 is a ‘factor’ of 60.

Key Vocabulary for this lesson

Multiple – The product of any number and a whole number is a multiple

When we say that 25 is ‘divisible’ by 5, that means that 25 is a ‘multiple’ of 5.

Key Vocabulary for this lesson

Key Vocabulary for this lesson

Prime Number - A whole number that is divisible by exactly two numbers: itself and 1.

or

A whole number greater than one that has exactly two factors, itself and 1.

Composite Number - Any number that is divisible by more than two numbers

or

A number, greater than one, that has more than two whole-number factors.

Key Vocabulary for this lesson

OBJECTIVE FOR THIS LESSON:

Each student will be able to:

Tell whether any number between 1-100 is prime or composite.

Let’s review Prime Numbers.

Every number is divisible by 1 and by itself.

A prime number is divisible ONLY by itself and 1. A prime number has ONLY two factors: itself and 1.

If a number isn’t prime it is composite.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

Prime Numbers between 1 and 50 are ----------

in Gray

We don’t need to memorize all prime numbers.

But we must be have a strategy for telling prime numbers from composite numbers.

Using the divisibility rules helps. Let’s discuss one more rule…

A number is divisible by:

4 if the last two digits form a

number that is divisible by 4.

Example:8112 is divisible by 4, because its last 2 digits ‘12’ is.

But what about the rules for 7 and 8? We haven’t discussed those.

There are also rules for 11, 12, 13 and larger numbers.

The rules for these numbers are not as simple to use.

As for 7 and 8 rules, my best suggestion is simply to memorize your multiplication tables up to 7 X12 and 8 X12.

That will cover your needs in just about every case.

Guided Practice:

Tell whether each number is a prime or composite number.

1. 87

2. 49

3. 93

4. 68

Guided Practice:

1. Is 87 prime or composite?

First use the simplest divisibility rules.

•Its odd, so it is not divisible by 2.

•Its digits, 8+7, add up to 15, so it is divisible by 3.

That means 87 is composite.

Guided Practice:

2. Is 49 is prime or composite?

If you have memorized 7 x 7 = 49, you will know that it is composite.

Better memorize

All multiplication facts!

Guided Practice:

1. Is 93 prime or composite?

•Its odd, so it is not divisible by 2.

•Its digits, 9+3, add up to 12, so it is divisible by 3.

That means 93 is composite.

Guided Practice:

1. Is 68 prime or composite?

•Since it is an even number, it is divisible by 2.

That means 68 is composite.

Challenge:

Tell whether 281 is prime or composite.

First use the simplest divisibility rules.

• Its odd, so it is not divisible by 2.• 2+8+1=11, so it is not divisible by 3.• 281 is not divisible by 4

(Go to slide 18 and look at the rule.)

• 281 is not divisible by 5.

Challenge:

Tell whether 281 is prime or composite.

• It is not divisible by 6

since it isn’t divisible by 2 or 3.

• It is not divisible by 9 since the digits 2+8+1=11.

By the way-Since we already checked and

found 281 is not divisible by 3, we know it cannot be divisible by 9 either .

Every number that is divisible by 9 is also divisible by 3.

Is it divisible by 8?

• Every multiple of 8 is an even number.

• So if it is an odd number it cannot be a multiple of eight and is not divisible by 8.

(Saying a number is a ‘multiple of eight’ means it is ‘divisible by 8’.)

Challenge: Tell whether 281 is prime or composite.

Challenge: Tell whether 281 is prime or composite.

Is it divisible by 7?

To find out, just divide by 7. (It must have no remainder.)

7)281 Since there is a remainder of 1, it is not divisible by 7.

281 is a Prime Number

That was a tough example.

Don’t worry…

In Math Level 6, you must only be able to tell whether numbers between 1-100 are prime or composite.

Independent Practice:

Tell whether each is prime or composite.

1. 9

2. 51

3. 37

4. 53

Pause the lesson while you complete the independent practice.

Independent Practice Answers

1. 9 is composite. 3x3=9. So it is divisible by 3.

2. 51 is composite. It is divisible by 3 since 5+1=6. (6 is a multiple of 3.)

3. 37 is prime. It is not divisible by 2,3,4,5,6,7,8,9,or any other number (except 37 and 1).

Conclusion:• Every whole number is either prime or

composite.• A prime number has no factors

besides the number itself and 1.• Composite numbers have more than 2

factors.• Saying a number is “a multiple of”

another number is the same as saying it “is divisible by” the other number.

Assignments-

1. Explain how to determine whether a number is prime or composite. Is 97 prime or composite?

Assignments-

2. By which of the following is 852 not divisible?

3. Explain how to determine whether a number is divisible by 6. Is 1638 divisible by 6? Is 12,680 divisible by 6?

Assignments-

3-Complete the attached assignment.Identify all numbers between 1-100 as prime or composite.