1. Multiples, Factors and Primes

2. Multiples A multiple of a number is found by multiplying the number by any whole number. What are the first six multiples of 4? To find the first six multiples of 4 multiply 4 by 1, 2, 3, 4, 5 and 6 in turn to get: 4,8,12,16,20and 24. Any given number has infinitely many multiples.

3. The lowest common multiple The lowest common multiple (or LCM) of two numbers is the smallest number that is a multiple of both the numbers. We can find this by writing down the first few multiples for both numbers until we find a number that is in both lists. For example: Multiples of 20 are :20,40,60,80, 100, 120,... Multiples of 25 are :25,50,75,100,125,... The LCM of 20 and 25 is100.

4. Finding factors A factor is a whole number that divides exactly into a given number. Factors come in pairs. For example, what are the factors of 30? 1 and30,2 and15,3 and10,5 and6. So, in order, the factors of 30 are: 1,2,3,5,6,10,15and 30.

5. The highest common factor The highest common factor (or HCF) of two numbers is the highest number that is a factor of both numbers. We can find the highest common factor of two numbers by writing down all their factors and finding the largest factor in both lists. For example: Factors of 36 are :1,2,3,4,6,9,12,18,36. Factors of 45 are :1,3,5,9,15, 45. The HCF of 36 and 45 is9.9.

6. Prime numbers If a whole number has two, and only two, factors it is called a prime number. For example, the number 17 has only two factors, 1 and 17. Therefore, 17 is a prime number. The number 1 has only one factor, 1. Therefore, 1 is not a prime number. There is only one even prime number. What is it? 2 is the only even prime number.

7. The first 10 prime numbers are: Prime numbers 2 357111317192329

8. Square numbers When we multiply a number by itself we say that we are squaring the number. To square a number we can write a small 2 after it. For example, the number 3 multiplied by itself can be written as: 3 × 3 or 3 2 Three squared The value of three squared is 9. The result of any whole number multiplied by itself is called a square number.

9. Square numbers Here are the first 10 square numbers: 1 2 = 1 × 1 =1 2 2 = 2 × 2 =4 3 2 = 3 × 3 =9 4 2 = 4 × 4 =16 5 2 = 5 × 5 =25 6 2 = 6 × 6 =36 7 2 = 7 × 7 =49 8 2 = 8 × 8 =64 9 2 = 9 × 9 =81 10 2 = 10 × 10 =100 + 3+ 5+ 7+ 9+ 11+ 13+ 15+ 17+ 19

10. Finding the square root is the opposite of finding the square: 8 squared 64 square rooted We write:  64 = 8 The square root of 64 is 8. Square roots

11. Now try these: 1.Write down the first 5 multiples of 14. 2.Which of these numbers are multiples of 5: 35, 157, 240, 475, 554? 3.Find all the factors of: a) 12 b) 20 c) 32 d) 24 e) 27 4.Find the LCM of 5 and 7 5.Find the LCM of 3, 5 and 6 6.Find the first 12 square numbers. Learn them. 7.What is the square root of: a) 36b) 169 c) 225 d) 144

12. Answers: 1.14; 28; 42; 56; 70 2.5; 35; 240; 475; 3.a) 12 – 1; 2; 3; 4; 6; 12 b) 20 – 1, 2, 4, 5, 10, 20 c) 32 – 1, 2, 4, 8, 16, 32 d) 24 – 1, 2, 3, 4, 6, 8, 12, 24 e) 27 – 1, 3, 9, 27 4.35 5.30 6.1; 4; 9; 16; 25; 36; 49; 64; 81; 100; 121; 7.a) 6 b) 13c) 15d) 12