9514 1404 393
Answer:
3 solutions: 1368, 5364, 9360
Step-by-step explanation:
In order to be divisible by 36, the number must be divisible by 9 and by 4. The number will be divisible by 9 if the sum of its digits is divisible by 9. 36 already has a digit sum of 9, so the two added digits must sum to 9.
The number will be divisible by 4 if the least-significant digit is a multiple of 4. That is, it must be 0, 4, or 8. Then the corresponding most-significant digits must be 9, 5, or 1.
The three solutions are ...
1368 = 38 · 36
5364 = 149 · 36
9360 = 260 · 36
