Question

Find the HCF of 52 & 117 & express it in form 52x + 117y..

Answer 1

Answer:

13 = HCF(52,117) = 52×(-2) + 117×1

Note:

• HCF ( or GCD ) 'd' of a and b (not both of which are zero) can be expressed in the form of ;

d = xa + yb , where x , y are integers .

• Dividend = Divisor•Quotient + Remainder

Solution:

Let's find the HCF of 52 and 117 using long division method .

52 ) 117 ( 2

-104

13 ) 52 ( 4

- 52

××

Hence,

HCF(52,117) = 13

From the division performed above , we have ;

117 = 2×52 + 13 --------(1)

52 = 4×13 + 0 --------(2)

From eq-(1) , we have ;

117 = 52×2 + 13

=> 13 = 117 – 52×2

=> 13 = 52×(-2) + 117×1

=> HCF(52,117) = 52×(-2) + 117×1 -------(3)

From eq-(3) , it is clear that ;

HCF(52,117) is in the form of 52x + 117y

where x = -2 and y = 1