example of a number that is divisible by 2,3 and 4, and that is formed by five non-zero digits.

1. A number is divisible by 2 if its last digit is even.
2. A number is divisible by 3 if the sum of its digits is divisible by 3.
3. A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

We choose five distinct non-zero digits to ensure a five-digit number. Let's choose the digits 2, 4, 6, 3, and 5.

Check divisibility:
- For 2: the last digit is 6 (even).
- For 3: sum of the digits: 2 + 6 + 4 + 3 + 5 = 20 which is not divisible by 3, so adjust.
Choose digits: 2, 6, 4, 3, 6.
Sum of digits: 2 + 6 + 4 + 3 + 6 = 21 which is divisible by 3.
- For 4: the last two digits are 36 which is divisible by 4.

So, the chosen number 26436 satisfies all conditions.

Answer:

26436