Coursework Notes - Number

Highest Common Factor (H.C.F.)

The HCF(highest common factor) of two (or more) numbers is the highest number that will divide into each of them exactly.

the HCF of 15, 25, 40 is ........5

example#1 - find the HCF of the following: ............36, 50

First find the factors by dividing the numbers by prime numbers, 2, 3, 5 etc. to reduce them to '1',

 2 36 2 50 2 18 5 25 3 9 5 5 3 3 1 1

36 = 3 x 3 x 2 x 2

50 = 2 x 5 x 5

The number that divides into both is 2 .

36 = 3 x 3 x 2 x 2..................50 = 2 x 5 x 5

(divides 3 x 3 x 2 =18 times) .................(divides 5 x 5 = 25 times)

So the HCF of 36 & 50 is ...2

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example#2 - find the HCF of the following: ............54, 96

First find the factors by dividing the numbers by prime numbers, 2, 3, 5 etc. to reduce them to '1',

 2 54 2 96 3 27 2 48 3 9 2 24 3 3 2 12 1 2 6 3 3 1

54 = 2 x 3 x 3 x 3

96 = 2 x 2 x 2 x 2 x 2 x 3

The number that divides into both is 2 x 3 .

54 = 2 x 3 x 3 x 3.................96 = 2 x 2 x 2 x 2 x 2 x 3

(divides 3 x 3 = 9 times) .................(divides 2 x 2 x 2 x 2 = 16 times)

So the HCF of 54 & 96 is ...2 x 3 = 6

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example#3 - find the HCF of the following: ............48, 256

First find the factors by dividing the numbers by prime numbers, 2, 3, 5 etc. to reduce them to '1',

 2 48 2 256 2 24 2 128 2 12 2 64 2 6 2 32 3 3 2 16 1 2 8 2 4 2 2 1

48 = 2 x 2 x 2 x 2 x 3

256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

The number that divides into both is 2 x 2 x 2 x 2 .

48 =2 x 2 x 2 x 2 x 3...............256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

(divides 3 times) .................(divides 2 x 2 x 2 x 2 = 16 times)

So the HCF of 48 & 256 is .... 2 x 2 x 2 x 2 = 16

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