The number of two digit numbers which are divisible by the sum of their digits is

Correct Answer: 23

Solution

Checking the two digit numbers by writing each as $$10a+b$$ and testing divisibility by $$a+b$$ gives the valid numbers $$10,12,18,20,21,24,27,30,36,40,42,45,48,50,54,60,63,70,72,80,81,84,90$$. There are $$23$$ such numbers.

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