Use Euclid division algorithm to find the hcf of 726&275
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For every single point of integers a and b there exists a unique integer Q and r such that a = bq + r
Where 0 ≤ r < b and here a > b.
We always divide the smaller number by the larger number.
Proceeding with Euclid division we have:
726/275 = 2 rem 99
726 = 275 × 2 + 176
275/176 = 1 rem 99
275 = 176 × 1 + 99
176/99 = 1 rem 77
176 = 99 × 1 + 77
99/77 = 1 rem 22
99 = 77 × 1 +22
77/2 = 3 rem 11
77 = 22 × 3 + 11
22/11 = 2 rem 0
22 = 11 ×2 +0
HCF = 11 Since here the remainder is zero.
We want to write it in the form :
726m + 275n = 11
We find the relationship of 726 and 275 in terms of ratio.
726/275 =66:25
66+25=91 = total ratio.
Meaning :
726/91 + 275/91 = 11
726m = 726/91
m = 1/91
275n =275/91
n = 1/91
So :
n = m = 1/91
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