Question

Express the hcf of 48 and 72as a linear combination

Answer 1

Answer:

HCF(48,72) = 24 = 72 - 48

Note:

HCF of two numbers a and b (not both of which are zero) can be written as their linear combination , ie ; HCF(a,b) = xa + yb

Solution:

We need to find HCF of 48 and 72 and express it as their linear combination.

Let's find the HCF of 48 and 72 using long division method.

48 ) 72 ( 1

- 48

24 ) 48 ( 2

- 48

××

Hence,

HCF(48,72) = 24

Now,

Observing the division , we have ;

72 = 1×48 + 24 -------(1)

48 = 2×24 + 0 -------(2)

From eq-(2) , it is clear that ;

HCF is 24.

Now,

From eq-(1) , we have ;

=> 72 = 1×48 + 24

=> 24 = 72 - 1×48

=> 24 = 72×1 + 48×(-1)

=> 24 = 72x + 48y , where x = 1 and y = -1

Clearly , HCF(48,72) ie; 24 = 72 - 48