if d is the hcf of 468 and 222 find the value of integers x and y which satisfy d = 468x + 222y
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32
222 l 468 l 2
-444
____
24 l 222 l 9
-216
_____
6 | 24 | 4
- 24
____
0
468 = 222(2) + 24
222 = 24(9) + 6
24 = 6(4) + 0
hcf= 6
6= 222-24(9)
= 222-{468-222(2)}(9)
= 222-468(9)+222(18)
= 222(19)-468(9)
=468(-9)+222(19)
a/q, 468(-9)+222(19)=468x+222y
=> x=(-9), y=19
-444
____
24 l 222 l 9
-216
_____
6 | 24 | 4
- 24
____
0
468 = 222(2) + 24
222 = 24(9) + 6
24 = 6(4) + 0
hcf= 6
6= 222-24(9)
= 222-{468-222(2)}(9)
= 222-468(9)+222(18)
= 222(19)-468(9)
=468(-9)+222(19)
a/q, 468(-9)+222(19)=468x+222y
=> x=(-9), y=19
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