Today Puzzle #781
Puzzle No. 781鈥� Monday 13 July
Professor Dodo’s landline number consists of 6 digits. If he forgets it he can easily reconstruct it as it is divisible without remainder by every number from 1 to 16 inclusive. What is his number?
Today’s #PuzzleForToday has been set by Chris Maslanka writer and broadcaster, specialising in puzzles and problem solving
Click here for the answer
Dodo's phone number has to be divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 & 6. Break down each of these factors into products of prime numbers: 2, 3, 2 X 2, 5, 2 X 3, 7, 2 X 2 X 2, 3 X 3, 2 X 5, 11, 2 X 2 X 3, 13, 2 X 7, 3 X 5 and 2 X 2 X 2 X 2.
The smallest set we can construct so that each entry in that list of numbers may be found is (2 X 2 X 2 X 2) X (3 X 3) X 5 X 7 X 11 X 13 = 720720; so that is the smallest number divisible by all the numbers from 1-16 and hence Dodo's number.
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