What is the sum of the digits of the decimal form of the number represented by brain teaser 22/11/2024 ![]() ![]() If you have an easily-factored number - and the easiest number to factor is 2 n - then it is easy to figure out the digit root recursively: 2 16 = 2 8 * 2 8, so DigitRoot(2 16) = DigitRoot(DigitRoot(2 8) * DigitRoot(2 8)) - We just made the problem much smaller. (Exercise to the reader: prove it! Hint: start by proving the same identity for addition.) The trick is: If you have Z = X * Y then DigitRoot(Z) = DigitRoot(DigitRoot(X) * DigitRoot(Y)). ![]() The digit sum of 65536 is 25, so the digit root is 2 + 5 = 7. The digit root is what you get when you repeat the digit sum until there's only one digit. The base 10 digit sum of 1024 is 1 + 2 + 4 = 7. The digit sum is, as you say, simply the sum of all the digits. However, there is an easy trick for finding the base 10 digit root of a number. There is no general trick I'm aware of for finding the base 10 digit sum of a number. ![]()
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