Divisibility

DIVISIBILITY

Any Interger I, when divided by a natural  number N, there exist a quotient Q and reminder R,
respectively.

I = QN + R

Theorems of divisibility:
1. If a is divisible by b then a.c is also divisible by b.
2. If a is divisible by b, b is divisible by c then a is divisible by c.
3. If a & b are natural numbers such that a is divisible by b and b is divisible by a then a = b.
4. If n is divisible by d and m is divisible by d then (m+n) and (m-n) also divisible by d.
      ex: 28, 742 both are divisible by 7, hence (28 + 742) and (28 - 742) are divisible by 7.