I wanted to know why if the number ends with 

0, 2, 4, 6, or 8 is even
 and if starts with 1,3, 5, 7, or 9 is odd 

I think if we know why if the number endswith 0 is always even will answer this 

because from addition rules 

even + even = even
even + odd = odd 

so always we have to split the number into sum for ex:

5425 = 5420 + 5 

which is even + odd = odd 

but why having 5420 **0** at the beginning made it even number 

++++++++++++++++++++++
edit:

why this rule doesn't apply on numbers which are divisible by 3 or 4