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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

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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.

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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

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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

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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?

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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?

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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?

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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.

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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.

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

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

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

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

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

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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.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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.

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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

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

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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

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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

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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

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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

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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

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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

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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

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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

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