How many different $4$-digit integers have the product of their digits equal to $5!$? What is the largest of these integers?
I know $5!$ is $120$, but I'm really stuck.
2026-05-14 06:18:00.1778739480
How many $4$ digit integers have the product of their digits equal to $5!$?
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Hints :
$120 = 1\cdot 2^{3}\cdot 3\cdot 5$. So possible digits are : $1,2,3,4,5,6,8.$
You may assume that there is $8$ in your number and amount possible situations.
After assume there $6$ and so on.