Question

Use Euclid's algorithm to find HCF of 1651 and 2032. Express the HCF in the form 1651m+2032n.

Answer 1

Answer:

127

Explanation-

We know that,

Euclid's division algorithm states that

a=bq+r where 0≤r<b

So,

2032=1651×1+381

1651=381×4+127

381=127×3+0

So, H.C.F. of 1651 and 2032 is 127.

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Hope it helps.

Answer 2

Answer:

Let a = 2032 and b = 1651

According to Euclid's division algorithm

a = bq + r { where, 0 ≤ r ≤ b }

=> 2032 = 1651 × 1 + 381 ---> (1)

=> 1651 = 381 × 4 + 127 ---> (2)

=> 381 = 127 × 3 + 0

H.C.F = 127

Now,

Expressing 127 in the form of 1651 m + 2032 n

127 = 1651 - 381 × 4 {using ( 2 )}

= 1651 - (2032 - 1651 × 1) × 4 {using ( 1 )}

= 1651 - (2032 - 1651) × 4

= 1651 - 2032 × 4 + 1651 × 4

= 1651 + 1651 × 4 - 2032 × 4

= 1651 (1 + 4) - 2032 × 4

= 1651 × (5) + 2032 × (- 4)

Comparing in the form 1651 m + 2032 n

• m = 5
• n = (- 4)