Division

Let are integers

• if there is an integer such that , then we say a divides b
  • a is a factor of b
  • b is a multiple of a
• If remainder is 0, then
• if and , then
• if then for all int
• if and then

“Assume . Then by def. divides s.t. “

Division Algorithm

“Not an algorithm” The Division Algorithm: Suppose a is an integer and d is a positive integer. There are unique integers q and r, with 0 ≤ r < d, such that a=dq+r

• d is the divisor
• a is the dividend
• q is the quotient
• r is the remainder

Note the following:

• q = a div d is used to express the quotient
• r = a mod d is used to express the remainder.