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2 years ago

7

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

1 answer:

vaieri [72.5K]2 years ago

6 0

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

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