Question

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

Answer 1

Solution:-

By Euclid's Division Lemma 117 > 52

117 = (52 × 2) + 13 (52 is the divisor)

52 = 13 × 4 + 0 ; The division process ends here, as remainder is 0. So, HCF is 13 (Here, 13 is divisor)

13 can also be expressed as 52x + 117y i.e. as 52 (-2) + 117 (1)

Answer 2

●STEP 1● : USING EUCLID'S DIVISION ALGORITHM TO FIND THE HCF OF 52 AND 117

》117 = 52 ×2 + 13 ____eqn(1)

》52 = 13 ×4 + 0

We get;

HCF(117,52)=13

●STEP 2●: Expressing HCF of 52 and 117 in the form 52x+117y using eqn(1)

We have eqn (1) as:

117=52×2+13

117 - (52×2) =13

13= 117 (1)+52 (-2)

It is the required answer where

x= -2 and y=1.