UNCORRECTEDSAMPLEPAGES

■ The number 1 is neither a prime nor a composite number.

■ The number 2 is prime. It is the only even prime number.

VIDEO DEMO

Building Understanding

1 The factors of 12 are 1, 2, 3, 4, 6 and 12. Is 12 a prime number?

2 The factors of 13 are 1 and 13. Is 13 a prime number?

3 State the first 10 prime numbers.

4 State the first 10 composite numbers.

5 What is the first prime number greater than 100?

6 Explain why 201 is not the first prime number greater than 200

Example 8

Determining whether a number is a prime or composite

State whether each of these numbers is a prime or composite: 22, 35, 17, 11, 9, 5

Prime: 5, 11, 17

Now you try

, 11, 17 have only two factors (1 and itself).

State whether each of these numbers is prime or composite: 19, 32, 13, 79, 57, 95

Example 9

Finding prime factors

Find the prime factors of 30.

SOLUTION EXPLANATION

Factors of 30 are:1, 2, 3, 5, 6, 10, 15, 30

Prime numbers from this list of factors are 2, 3 and 5.

Now you try

Find the prime factors of 84

Find the entire set of factors first.

Include only the prime numbers in your list.

Exercise 2D

1 State whether each of the following is a prime (P) or composite (C) number.

24

2 State whether each of the following is a prime (P) or composite (C) number.

23

31

3 Find the prime factors of:

39

4 List the composite numbers between, but not including:

50

5 The following are not prime numbers, yet they are the product (×) of two primes. Find the two primes for each of the following numbers.

55

91

143

6 Which one of these composite numbers has the fewest prime factors? 12, 14, 16, 18, 20

7 Twin primes are pairs of primes that are separated from each other by only one even number; for example, 3 and 5 are twin primes. Find three more pairs of twin primes.

8 13 and 31 are known as a pair of ‘reverse numbers’. They are also both prime numbers. Find any other two-digit pairs of prime reverse numbers.

9 Many mathematicians believe that every even number greater than 2 is the sum of two prime numbers. For example, 28 is 11 + 17. Show how each of the even numbers between 30 and 50 can be written as the sum of two primes.

10

Give two examples of a pair of primes that add to a prime number. Explain why all possible pairs of primes that add to a prime must contain the number 2.

11 Find three different prime numbers that are less than 100 and which sum to a fourth different prime number. There are more than 800 possible answers. See how many you can find.

ENRICHMENT: Prime or not prime? – – 12

12 Design a spreadsheet that will check whether or not any number entered between 1 and 1000 is a prime number.