Why numbers with 0 as it’s unit digit are even

Question

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

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edit:

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

Answer 1

Thanks to all comments

the answer as i got is :

for the first section:-

all the numbers that has unit digit 0 are divisibe by 10 which is divisible by 2 so it's even

for the second section:- i think it's about the Cyclicity of the numbers 3 and 4

if the number is divisible by 3 by division theorem

x = 3*r for any r in N

if we traced the Cyclicity of 3 we will find that

3*0 = 0 , 3*1 = 3 , 3*2 = 6 , 3*3 = 9 .....etc

it will be 0,3,6,9,2,5,8,1,4,7

which are not always even or add

if someone have any comment please tell :)