Question

Use Euclid algorithm lemma to find HCF of 1651 and 2032 express the HCF in the form 1651M +2032N

Answer 1

We know, Euclid algorithm lemma , a = bq + r where 0 ≤ r < b
From Euclid algorithm lemma , 2032 = 1651 × 1 + 381
again, using lemma for 1651 and 381 , e.g., 1651 = 381 × 4 + 127
similarly use lemma for 381 and 127 , e.g., 381 = 127 × 3 + 0
Hence, HCF = 127

Now, 127 = 1651M + 2032N
⇒127 = (127 × 13)M + (127 × 16)M
⇒1 = 13M + 16N
Here many solutions possible because we have one equation contains two variable .
If I assume M = 5 and N = -4
Then, 13 × 5 + 16 × -4 = 65 - 64 = 1
So, HCF of 1651 and 2032 in the form of 1651M + 2032N is [1651(5) + 2032(-4)]

Answer 2

Answer:

see the attachment friend

Hope it helps you