Division Algorithm

The Division Algorithm is a fundamental concept in mathematics, particularly in number theory. It states that for any two integers, \( a \) (the dividend) and \( b \) (the divisor), where \( b \) is positive, there exist unique integers \( q \) (the quotient) and \( r \) (the remainder) such that \( a = bq + r \). Here, \( r \) is always less than \( b \). This means you can divide any number by another and express it in terms of how many times the divisor fits into the dividend, plus what’s left over.