Answer:
Since 2032 gt 1651, we divide 2032 by 1651 to get 1 as quotient and 381 as remainder. step 2. Since the remainder 381≠0 , we divide 1651 by 381 to get 4 as quotient and 127 as remainder.
Step-by-step explanation:
Euclid algorithm lemma, a = bq + r where 0 ≤ r < b
From Euclid algorithm lemma, 2032 = 1651 × 1 + 381
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 + 2032 N
⇒127 = (127 × 13)M + (127 × 16)M
⇒1 = 13M + 16 N
Here many solutions possible because we have one equation contains two variable.
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 + 2032 N is [1651(5) + 2032(-4)]
