Question

Write one digit on each side of 36 to make a four-digit multiple of 36. How many different solutions does this problem have?

Answer 1

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