A positive integer K is written on a blackboard. When its rightmost digit is erased, the number remaining is K / 14. What number is K? Find all possibilities

any help would be great

2. Originally Posted by Chuck_3000
A positive integer K is written on a blackboard. When its rightmost digit is erased, the number remaining is K / 14. What number is K? Find all possibilities

any help would be great
Given a number K, let the last digit be "a". Thus we know that $\frac{K-a}{10} = \frac{K}{14}$. This leads to the equation $K = \frac{7}{2}a$.

Now, K must be a multiple of 14. Thus a can take on the values 0, 2, 4, 6, 8. Thus the only possible K values are 0, 7, 14, 21, 28. Of these only two are divisible by 14, so the answers are 14 and 28.

-Dan