Digits multiplying to half the number

MediumBrainteasers~4m

There is a unique two-digit positive integer whose two digits, when multiplied together, give exactly half the integer itself. What is that integer?

Show hints (2)+
  1. Let the number be 10a+b10a+b; the condition is ab=(10a+b)/2ab=(10a+b)/2.
  2. Rearrange to b=10a/(2a1)b=10a/(2a-1) and test digits - only one aa gives an integer.

Answer

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36

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