Henry Ernest Dudeney/Modern Puzzles/62 - Factorizing

Modern Puzzles by Henry Ernest Dudeney: $62$

Factorizing

What are the factors (the numbers that will divide it without any remainder) of this number -- $1000000000001$?

This is easily done if you happen to know something about numbers of this peculiar form.

In fact, it is just as easy for me to give two factors if you insert, say $101$ noughts, instead of $11$, between the two ones.

There is a curious, easy, and beautiful rule for these cases.

Can you find it?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $62$. -- Factorizing
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $113$. Factorizing