If the hcf of 85 and 51 is expressible as 85x +51y then y=?
Answers
Answer:
Step-by-step explanation:
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
Given,
Number 1 = 85
Number 2 = 51
The HCF is expressible as 85x +51y
To Find,
y =?
Solution,
As we can see 51 < 85, using Euclid’s division we get,
85 = 51*1 + 34
The remainder 34 ≠ 0, therefore applying Euclid’s division again
51 = 34*1 + 17
The remainder 17 ≠ 0, therefore applying Euclid’s division again
34=17*2+0
The remainder is equal to 0. The iteration stops at the third step.
The HCF = The divisor at the last stage
The HCF = 17
Therefore, according to the question,
17=[51-34*1] [From second step]
17=[51-{85-(51*1)}*1]
17=[51-85*1+51*1]
17=[51*2-85*1]
17=[(-85*1)+51*2]
Comparing this with 85x +51y, we get
Therefore, x = -1 and y = 2
Hence, the value of y = 2.