Well I'm working on some mathematics aptitude problem on divisibility. There are certain divisibility rules for numbers 6, 12, 15 etc. which are
- If n is divisible by 2 and 3, it is divisible by 6
- If n is divisible by 3 and 4, it is divisible by 12
- If n is divisible by 3 and 5, it is divisible by 15
So, I applied the above rule on 8 and thought
- If n is divisible by 2 and 4, it is divisible by 8
but I found a counterexample 576484 to my intuition and it bust the bubble of my figment. It is divisible by 2 and as well by 4, but not by 8.
Why then it is not divisible by 8? If it is simultaneously divisible by 2 and 4.
Doesn't the rule applies in this case as well? Just like they are applied in the cases of 6, 12, & 15. That is, if factors 'a' and 'b' of number 'n' divides a given number 'm', then 'n' also divides 'm'.