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3. Factors Factors and Multiples If one number divides another number without remainder then it is a factor of the number. Example 1: The factors of 10 are: 1, 2, 5, and 10 since: 10  1 = 10 10  2 = 510  5 = 210  10 = 1 Example 2: The factors of 15 are: 1, 3, 5, and 15 since: 15  1 = 15 15  3 = 515  5 = 315  15 = 1 17  1 = 17 17  17 = 1 Example 3: The factors of 17 are: 1, and 17 since: A prime number has only 2 factors, 1 and itself

4. Factors and Multiples Find the factors of the following: 8121518 24303157 50568199 abcd efgh ijkl 1,2,4,81,2,3,4,6,121,3,5,151,2,3,6,9,18 1,2,3,4,6,8,12,241,2,3,5,6,10,15,30 1,31 1,2,5,10,25,501,2,4,7,8,14,28 1,3,9,27,811,3,9,11,33,99 1,3,19,57 If one number divides another number without remainder then it is a factor of the number.

5. Factors and Multiples Some of the numbers in the pentagons are factors of the number in the central decagon. Which ones? 52 13 4 9 7 8 26 20 2 6 12

6. Factors and Multiples Some of the numbers in the pentagons are factors of the number in the central decagon. Which ones? 36 13 15 18 7 3 9 20 14 6 16

7. Factors and Multiples 64 32 10 18 8 4 9 24 14 6 16 Some of the numbers in the pentagons are factors of the number in the central decagon. Which ones?

8. Factors and Multiples 84 32 12 15 8 4 3 28 14 6 16 Some of the numbers in the pentagons are factors of the number in the central decagon. Which ones?

9. Factors and Multiples 144 36 12 74 8 2 4 28 14 72 18 Some of the numbers in the pentagons are factors of the number in the central decagon. Which ones?

10. Prime Factors Factors and Multiples A prime number which divides into another number without leaving a remainder is called a prime factor of the number. Example 1: The prime factors of 12 are 2 and 3 since both of these are prime numbers that divide 12. Example 2: The prime factors of 15 are 3 and 5 since both of these are prime numbers that divide 15. Example 3: The prime factors of 42 are 2,3, and 7since these are prime numbers that divide 42. Example 4: The prime factors of 55 are 5 an 11 since these are prime numbers that divide 55.

11. Factors and Multiples Find the prime factors of the following: 16202425 28493623 3042110210 abcd efgh ijkl 22 and 52 and 35 2 and 772 and 323 2, 3, and 52, 3 and 72, 5, and 112,3,5 and 7 A prime number which divides into another number without leaving a remainder is called a prime factor of the number.

12. Factors and Multiples Find prime factors of the number in the middle. 18 13 4 9 7 8 1 12 2 6 3

13. Factors and Multiples Find prime factors of the number in the middle. 30 15 4 5 7 10 1 30 2 6 3

14. Factors and Multiples Find prime factors of the number in the middle. 42 3 4 5 7 1 21 6 2 9

15. Factors and Multiples Find prime factors of the number in the middle. 77 10 4 5 7 42 11 77 6 2 3

16. Factors and Multiples Find prime factors of the number in the middle. 105 3 4 5 7 15 11 21 6 2 9

17. HCF Factors and Multiples The highest common factor (HCF) of two or more numbers is the largest factor that is common to them all. Example 1: The HCF of 12 and 18 is 6 since this is largest number that will divide both. Example 2: The HCF of 15 and 30 is 15 since this is largest number that will divide both. Example 3: The HCF of 23 and 18 is 1 since this is largest number that will divide both (23 is prime). Example 4: The HCF of 8, 12, 28 is 4 since this is largest number that will divide all three numbers.

18. The highest common factor (HCF) of two or more numbers is the largest factor that is common to them all. Find the HCF of the sets of numbers shown. HCF 9 and 15 HCF 12 and 30HCF 18 and 4 HCF 20 and 35 HCF 42 and 28HCF 36 and 27 HCF 9, 54, 18 HCF 24, 56, 16 HCF 60, 36, 24 3 62 5 14 9 9 8 12 a bc d e f g h i

19. Factors and Multiples Find the HCF of the two numbers shown in the middle. 10 12 6 9 7 8 5 1 2 4 10 12

20. Factors and Multiples Find the HCF of the two numbers shown in the middle. 12 6 9 7 8 5 1 2 4 10 20

21. Factors and Multiples Find the HCF of the two numbers shown in the middle. 15 25 7 9 35 3 5 15 2 4 10 35

22. Factors and Multiples Find the HCF of the two numbers shown in the middle. 20 18 12 36 9 5 15 2 4 10 36

23. Factors and Multiples Find the HCF of the two numbers shown in the middle. 72 24 18 12 36 9 8 15 2 4 10 48

24. Factors and Multiples Find the HCF of the three numbers shown in the middle. 18 24 18 12 28 2 8 15 6 4 9 28 48

25. Factors and Multiples Find the HCF of the three numbers shown in the middle. 18 24 18 12 36 2 8 15 6 4 9 36 48

26. Factors and Multiples Find the HCF of the three numbers shown in the middle. 60 24 4 12 30 20 9 15 6 5 10 90 105

27. Multiples Factors and Multiples If a number is multiplied by another whole number then the new number formed is a multiple of the original. Example 1: Some multiples of 3 are: 3, 6, 9, and 15 since: 1 x 3 = 3 2 x 3 = 63 x 3 = 95 x 3 = 15 3 x 8 = 245 x 8 = 408 x 8 = 6410 x8 = 80 Example 2: Some multiples of 8 are: 24, 40, 64, and 80 since: Example 3: The first 4 multiples of 9 are 9, 18, 27, 36 since: 1 x 9 = 92 x 9 = 183 x 9 = 274 x 9 = 36

28. Factors and Multiples Find the first four multiples of the following: 2345 6879 10111213 abcd efgh ijkl 2, 4, 6, 83, 6, 9, 124, 8, 12, 165, 10, 15, 20 6,12,18,24 8,16,24,32 7,14,21,28 10,20,30,4011,22,33,4412,24,36,4813,26,39,52 If a number is multiplied by another whole number then the new number formed is a multiple of the original. 9,18,27,36

29. Factors and Multiples Some of the numbers in the pentagons are multiples of the number in the central decagon. Which ones? 4 13 4 9 7 8 36 20 2 6 12

30. Factors and Multiples Some of the numbers in the pentagons are multiples of the number in the central decagon. Which ones? 9 13 4 9 54 18 36 20 2 6 12

31. Factors and Multiples Some of the numbers in the pentagons are multiples of the number in the central decagon. Which ones? 8 4 8 9 56 18 32 25 2 16 12

32. Factors and Multiples Some of the numbers in the pentagons are multiples of the number in the central decagon. Which ones? 6 8 8 9 54 19 3 36 2 16 14

33. LCM Factors and Multiples The lowest common multiple (LCM) of two or more numbers is the smallest number that they will all divide into evenly without leaving a remainder. Example 1: The LCM of 6 and 12 is 12 since 12 is the smallest number that both 6 and 12 divide into without remainder. Example 2: The LCM of 8 and 20 is 40 since 40 is the smallest number that both 8 and 20 divide into without remainder. Example 3: The LCM of 9 and 5 is 45 since 45 is the smallest number that both 9 and 5 divide into without remainder. Example 4: The LCM of 2, 3 and 8 is 24 since 24 is the smallest number that 2, 3 and 8 divide into without remainder.

34. Find the LCM of the sets of numbers shown. LCM 2 and 3 LCM 4 and 10LCM 6 and 18 LCM 9 and 36 LCM 7 and 9LCM 36 and 12 LCM 9, 54, 18 LCM 14, 28, 7 LCM 5, 6, 7 6 2018 36 63 36 54 28 210 The lowest common multiple (LCM) of two or more numbers is the smallest number that they will all divide into evenly without leaving a remainder. a bc d e f g h i

35. Factors and Multiples Find the LCM of the numbers shown in the centre. 4 12 4 9 7 8 36 24 2 6 12

36. Factors and Multiples Find the LCM of the numbers shown in the centre. 6 12 48 4 24 8 48 18 2 6 9 8

37. Factors and Multiples Find the LCM of the numbers shown in the centre. 3 20 48 4 24 30 60 15 5 6 3 4 5

38. Factors and Multiples Find the LCM of the numbers shown in the centre. 15 90 4 24 30 20 60 5 6 3 12 4

39. Find the factors of the following: 8121518 24303157 505681100 abcd efgh ijkl If one number divides another number without remainder then it is a factor of the number. Worksheet 1

40. Find the prime factors of the following: 16202425 28493623 3042110210 abcd efgh ijkl A prime number which divides into another number without leaving a remainder is called a prime factor of the number. Worksheet 2

41. The highest common factor (HCF) of two or more numbers is the largest factor that is common to them all. Find the HCF of the sets of numbers shown. HCF 9 and 15 HCF 12 and 30HCF 18 and 4 HCF 20 and 35 HCF 42 and 28HCF 36 and 27 HCF 9, 54, 18 HCF 24, 56, 16 HCF 60, 36, 24 a bc d e f g h i Worksheet 3

42. Find the first four multiples of the following: 2345 6879 10111213 abcd efgh ijkl If a number is multiplied by another whole number then the new number formed is a multiple of the original. Worksheet 4

43. Find the LCM of the sets of numbers shown. LCM 2 and 3 LCM 4 and 10LCM 6 and 18 LCM 9 and 36 LCM 7 and 9LCM 36 and 12 LCM 9, 54, 18 LCM 14, 28, 7 LCM 5, 6, 7 The lowest common multiple (LCM) of two or more numbers is the smallest number that they will all divide into evenly without leaving a remainder. a bc d e f g h i Worksheet 5