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# Prime and Composite Numbers, & Multiples ### Key Concepts

• Prime numbers
• Composite numbers

## Prime and Composite Numbers, Multiples

#### Prime number:

A prime number is a whole number greater than 1 that has exactly two factors, 1 and itself.

13 can only be factorized as follows:

1 × 13 = 13

13 × 1 =13

13 groups of 1

1 group of 13

This means 1 and 13 are the only factors of 13.

So, 13 is a prime number because it could not be divided into groups of equal numbers.

#### Composite number:

A composite number is a number greater than 1 that has more than two factors.

For example, 12 can be factorized in multiple ways.

So, the factors of 12 are 1, 2, 3, 4,6 and 12.

It has more than two factors. Therefore, 12 is a composite number.

### 7.2.1 Prime numbers

A prime number is a whole number greater than 1 that has exactly two factors, 1 and itself.

Example1:

Robert has 7 balls. Can he group the balls in more than two ways?

Solution:

7 is a prime number.

The number 1 is a special number. It is neither prime nor composite.

7 is a prime number.

So, he cannot group the balls in more than two ways.

Example2:

Ria has 11 balloons to decorate the room. Ria says, “I have prime number of balloons” is she correct? Explain.

Solution:

11 is a prime number.

### 7.2.2 Composite numbers

A composite number is a number greater than 1 that has more than two factors.

Example1:

The image shows 8 books. What are the factors for 8?

Solution:

8 is a composite number.

So, 8 is a composite number.

Example2:

Mart wants to buy 4 caps. Tell whether 4 is a prime or composite number.

Solution:

4 is a composite number.

## Exercise

1. John has 49 pencils. Can he group the pencils in more than two ways?
2. Tell whether each number is prime or composite.
1. 23
2. 34
3. 45
3. How many composite numbers are there between 1 to 50?
1. Circle the prime numbers.
2. List out the factors of a number and write whether the number is prime or composite.
1. 47 Factors are _______________
2. Is 47 is prime or composite? ______________.
3. What is the fifth prime number?
4. Find two prime numbers that add up to 52.
5. How many composite numbers are there between 50 to 80?
6. Routh says the product of two composite numbers must also be composite. Joan disagreed. Who is correct?
7. List out the factors of a number and write whether the number is prime or composite

### What have we learned:

• Understand prime numbers.
• Understand composite numbers.
• Finding factors for prime numbers.
• Finding factors for composite numbers.
• Identify the prime numbers and composite numbers.

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