What is the biggest fivedigit $abcde$ number, thats divisible by $bcde$, $cde$, $de$ and $e$?
I was trying to find it but I couldnt. Can you help me with a step by step answer?
2026-03-30 15:14:11.1774883651
What is the biggest fivedigit $abcde$ number, thats divisible by $bcde$, $cde$, $de$ and $e$?
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If $bcde$ divides $abcde$, it also divides $a0000$, or $a*2^4*5^4$. But since $e$ divides $abcde$, $e$ must not be zero, so $bcde$ is not divisible by $10$. So $bcde$ can have factors of $2$ or $5$ but not both, so it divides either $a*2^4$ or $a * 5^4$. The maximum value $bcde$ could be then is $9*5^4 = 5625$, which means $abcde$ would be $95625$. One can check that this works.