Question

Express the Hcf of 468 and 222 as 468x+ 222y where x,y are integers in 2 different ways.

Answer 1

Answer:

Step-by-step explanation:

468 = 2 x 2 x 3 x 3 x 13

222 = 2 x 3 x 37

HCF = 2 x 3 = 6

6 = 222 - 216

= 222 - (24) 9

= 222 - (468–444)9

= 222 - (468)9 + (444)9

= 222 - (468)9 + (222)(2)(9)

= 222 (19) - 468 (9)

= 468(-9) + 222(19)

6 = 468 x + 222 y …………(1)

The above is one way of expressing the HCF 6 of 468 and 222 where x = - 9 and y = 19

Now 6 = 468 (-9) + 222 (19) can be written as 468 (-9) + 222(19) + 468(222)-222(468)

= 468(213) + 222(-449)

= 468 X + 222 Y………(2)

Thus the HCF 6 has been expressed as

468 (-9) +222(19) as also 468(213)+222(-449) in two different ways.