Cambridge International Mathematics

Assumed Knowledge (Number) 7

For example: 2 24

2 12

2 6

3 3

1 ) 24 = 2£ 2 £ 2 £ 3

2 42

3 21

7 7

1 ) 42 = 2£ 3 £ 7

COMMON FACTORS AND HCF

Notice that 2 is a factor of both 24 and 42. We say that 2 is acommon factorof 24 and 42.

3 is also a common factor of 24 and 42 , which means the product 2 £3=6is another common factor.

Acommon factoris a number that is a factor of two or more other numbers.

Thehighest common factor (HCF)is the largest factor that is common to two or more numbers.

To find the highest common factor of a group of numbers it is often best to express the numbers as products

of prime factors. Then the common prime factors can be found and multiplied to give the HCF.

Example 9 Self Tutor

Find the highest common factor of 36 and 81.

So, 2 36 36 = 2£ 2 £ 3 £ 3

2 18

3 9

3 3

1

and 3 81 81 = 3£ 3 £ 3 £ 3

3 27

3 9

3 3 ) HCF=3£3=9

1

MULTIPLES

Amultipleof any positive integer is obtained by multiplying it by another positive integer.

For example, the multiples of 7 are 7 £1=7, 7 £2=14, 7 £3=21, 7 £4=28, ...... so we can list

them as 7 , 14 , 21 , 28 , 35 , ......

Example 10 Self Tutor

Find: a the largest multiple of 7 which is less than 300

b the smallest multiple of 7 which is greater than 500.

a 7 3020

42 with remainder 6

So, the largest multiple is

7 £42 = 294:

b 7 5010

71 with remainder 3

So, the smallest multiple is

7 £72 = 504:

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