Please teach and explain euclid's division lemma
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Euclid's Division Lemma:
Given integers a and b,there exist unique pair of integers q and r satisfying
a=bq+r , 0≤r<b
Example: i) 5 and 2
Here a=5 and b=2
5=2×2+1
Here q=2 and r=1 such that,
0<1<2.
ii)
108 and 12
Here a=108 and b=12
108=12×9+0
Here q=9 and r=0 such that,
0=0<12
Given integers a and b,there exist unique pair of integers q and r satisfying
a=bq+r , 0≤r<b
Example: i) 5 and 2
Here a=5 and b=2
5=2×2+1
Here q=2 and r=1 such that,
0<1<2.
ii)
108 and 12
Here a=108 and b=12
108=12×9+0
Here q=9 and r=0 such that,
0=0<12
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