Page 16 - Mathematics Coursebook

1.5 Prime numbers

) Exercise 1.5

1 There are two prime numbers between 20 and 30. What are they?
2 Write down the prime numbers between 30 and 40. How many are there?

3 How many prime numbers are there between 90 and 100?
4 Find the prime factors of each number.
a 10 b 15 c 25
d 28 e 45 f 70

5 a Find a sequence of five consecutive numbers,
none of which is prime. Numbers such as 1, 2, 3, 4, 5 are
b Can you find a sequence of seven such numbers? consecutive. 2, 4, 6, 8, 10 are

consecutive even numbers.
6 Look at this table.
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

a i Where are the multiples of 3? ii Where are the multiples of 6?
b In one column all the numbers are prime numbers. Which column is this?

c Add more rows to the table. Does the column identified in part b still contain only prime
numbers?
7 Each of the numbers in this box is the product of two prime
numbers. The product is the result of
multiplying numbers.
226 321 305 133

Find the two prime numbers in each case.

8 Hassan thinks he has discovered a way to find prime numbers. 11 11 + 2 = 13

11 11 + 2 = 13
Investigate whether Hassan is correct.
13
13 13 + 4 = 17
13 + 4 = 17
17 17 + 6 = 23...
I start with 11 and then add 2, then 4, 17 17 + 6 = 23...
then 6 and so on.
The answer is a prime number every time.

9 a Find two different prime numbers that add up to:
i 18 ii 26 iii 30.

b How many different pairs can you find for each of the numbers in part a?

1 Integers 15