Henry Ernest Dudeney/Modern Puzzles/97 - A Common Divisor

Modern Puzzles by Henry Ernest Dudeney: $97$

A Common Divisor

Here is a puzzle that has been the subject of frequent inquiries by correspondents,

only, of course, the actual figures are varied considerably.

A country newspaper stated that many schoolmasters have suffered in health in their attempts to master it!

Perhaps this is merely a little journalistic exaggeration, for it is really a very simple question if you only have the cunning to hit on the method of attacking it.

This is the question:

Find a common divisor for the three numbers $480 \, 608$, $508 \, 811$, and $723 \, 217$, so that the remainder shall be the same in every case.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $97$. -- A Common Divisor
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $179$. A Common Divisor