Use elucids algorithm to find the hcf of85 and 51 and express them in the form of 85x+51y where x and y are integers
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According to Euclid's division lemma
a=bq+r, 0<=r<b
85=51*1+34
51=34*1+17
34=17*2+0
17=[51-34*1]
17=[51-{85-(51*1)}*1]
17=[51-85*1+51*1]
17=[51*2-85*1]
17=[(-85*1)+51*2]
17=85x+51y
x = (-1), y = 2
a=bq+r, 0<=r<b
85=51*1+34
51=34*1+17
34=17*2+0
17=[51-34*1]
17=[51-{85-(51*1)}*1]
17=[51-85*1+51*1]
17=[51*2-85*1]
17=[(-85*1)+51*2]
17=85x+51y
x = (-1), y = 2
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HEYA!!!
HERE IS YOUR ANSWER,
=> HCF OF (85, 51)
=> 85 = 51×1 + 34 ---(i)
=> 51 = 34×1 + 17 ---(ii)
=> 34 = 17×2 + 0 ---(iii)
∵ HCF OF (85, 51) = 17
=> 17 = 51 - 34×1 [Using (ii)]
=> 17 = 51 - (85 - 51×1)×1 [Using (i)]
=> 17 = 51 - 85 + 51
=> 17 = 2×51 - 85
NOW,
=> On comparing with 85x + 51y, we get x = -1 and y = 2.
HOPE IT HELPS YOU,
THANK YOU.☺️☺️
HERE IS YOUR ANSWER,
=> HCF OF (85, 51)
=> 85 = 51×1 + 34 ---(i)
=> 51 = 34×1 + 17 ---(ii)
=> 34 = 17×2 + 0 ---(iii)
∵ HCF OF (85, 51) = 17
=> 17 = 51 - 34×1 [Using (ii)]
=> 17 = 51 - (85 - 51×1)×1 [Using (i)]
=> 17 = 51 - 85 + 51
=> 17 = 2×51 - 85
NOW,
=> On comparing with 85x + 51y, we get x = -1 and y = 2.
HOPE IT HELPS YOU,
THANK YOU.☺️☺️
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