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Division Algorithm

For $a$ and positive $b$ , unique $q,r$ exist with $a=bq+r$ and $0\le r<b$ .

The Division Algorithm guarantees, for any integer $a$ and positive integer $b$ , unique integers $q$ (quotient) and $r$ (remainder) with $a=bq+r$ and $0\le r<b$ .

Examples

For $a=47, b=5$ : $47=5(9)+2$ , so $q=9, r=2$ .