Express the HCF of 468 and 222 as 468x +222y where x and y are integers in two different ways.
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Using Euclid's division algorithm on 468,222 :
here, 468>222
∴, 468=222×2+24 -------(1)
222=24×9+6 --------------(2)
24=6×4+0
since the remainder is 0 now therefore HCF(468,222)=6
From (2) we have,
6=24×9-222
or, 6=-222+{468-(222×2)}×9
or, 6=468×9+222×(-1-2×9)
or, 6=468×9+222×(-1-18)
or, 6=468×9+222(-19)
∴, 6=468x+222y where x=9 and y=-19
here, 468>222
∴, 468=222×2+24 -------(1)
222=24×9+6 --------------(2)
24=6×4+0
since the remainder is 0 now therefore HCF(468,222)=6
From (2) we have,
6=24×9-222
or, 6=-222+{468-(222×2)}×9
or, 6=468×9+222×(-1-2×9)
or, 6=468×9+222×(-1-18)
or, 6=468×9+222(-19)
∴, 6=468x+222y where x=9 and y=-19
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