Goal: smallest 4-digit number using 1, 2, 3, 4 once, divisible by 4.
- Rule: A number is divisible by 4 if its last two digits form a multiple of 4.
- Form all possible last-two-digit pairs from 1, 2, 3, 4.
- Check which pairs are multiples of 4:
\(12\) is divisible by \(4\).
\(24\) is divisible by \(4\).
\(32\) is divisible by \(4\).
- So possible endings are:
\(\_\_12\), \(\_\_24\), \(\_\_32\).
- Make the smallest thousands and hundreds digits with the remaining numbers for each ending:
Ending \(12\): use \(3,4\) in front → \(3412\).
Ending \(24\): use \(1,3\) in front → \(1324\).
Ending \(32\): use \(1,4\) in front → \(1432\).
- Compare:
\(1324 < 1432 < 3412\).
- Smallest number is \(\boxed{1324}\).