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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

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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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