Divisors of One More than Power of 10/Number of Zero Digits Even/Examples
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Examples of Divisors of One More than Power of 10: Number of Zero Digits Even
\(\ds 11\) | \(=\) | \(\ds 11\) | ||||||||||||
\(\ds 1001\) | \(=\) | \(\ds 11 \times 91\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 7 \times 11 \times 13\) | ||||||||||||
\(\ds 100 \, 001\) | \(=\) | \(\ds 11 \times 9091\) | ||||||||||||
\(\ds 10 \, 000 \, 001\) | \(=\) | \(\ds 11 \times 909 \, 091\) | ||||||||||||
\(\ds 1 \, 000 \, 000 \, 001\) | \(=\) | \(\ds 11 \times 90 \, 909 \, 091\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 7 \times 11 \times 13 \times 19 \times 52 \, 579\) | ||||||||||||
\(\ds 100 \, 000 \, 000 \, 001\) | \(=\) | \(\ds 11 \times 9 \, 090 \, 909 \, 091\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 11^2 \times 23 \times 4093 \times 8779\) |
Demonstration
90909091 x 11 -------- 90909091 909090910 ----------- 1000000001
Also see
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $62$. -- Factorizing
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $113$. Factorizing