One of the often misunderstood concept in math is divisibility. Divisibility is different from the operation division.
The Solution describes 7 key properties of divisibility and proves them mathematically as why they are true.
The 7 divisibility properties follow:
(a) a|0, a|a
(b) a|1 if and only if a=±1
(c) if a|b and c|d, then ac|bd (for c?0)
(d) if a|b and b|c, then a|c (for b?0)
(e) (a|b and b|a) if and only if a=±b
(f) if a|b and b?0, then |a|?|b|
(g) if a|b and a|c, then a|(bx+cy) for any integers x,y.