Problem 8:
If $3$ and $4$ individually divides a number, then also divides that number. For example, all of $3, 4$ and $12$ divide $48$. But if a number is divisible by $3$ and $6$ individually it may or may not be divisible by $3 \times 6=18$ . For example, both of $54$ and $60$ are divisible by $3$ and $6$ individually, though only $54$ is divisible by $18$. Can you explain why this happens?
BdMO National Primary 2011/8
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
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Re: BdMO National Primary 2011/8
Because the mentioned rule is applicable only for co-prime numbers.
And prime power factorization is the main reason of any number divisibility by other numbers.
And prime power factorization is the main reason of any number divisibility by other numbers.