Question

Find the hcf of 657 and 963 express it in the form of 657m 963n and hence find the value of m and n

Answer 1

Answer: m = 22 and n = -15

Step-by-step explanation:

According to Euclid's division lemma

a=bq+r, 0<=r<b

963=657*1+306

657=306*2+45

306=45*6+36

45=36*1+9

36=9*4+0

therefore hcf of the two number is 9

9=[45-(36*1)]

9=[45-{306-(45*6)}*1]

9=[45-(306*1)+(45*6)]

9=[{657-(306*2)}*(6+1)-306*1]

9=[657*7-306*14-306*1]

9=[657*7-306*15]

9=[657*7-{963-(657*1)}*15]

9=[657*7-963*15+657*15]

9=[657*22-963*15]

9=657m+963n

m= 22, n = (-15)