141,421
141,421 is the first six digits of the square root of two.
- Odd
- Composite
Where 141,421 fits
Why 141,421 is special
Its irrationality was the first ever proved, and the proof is short enough to fit in a paragraph — which is why it is usually the first proof by contradiction anyone meets. It is also the ratio behind A-series paper: A4 halved along its long side gives two sheets of exactly the same proportions, which only works at this ratio.
141,421 is part of
Factors & digit properties
- Divisors (8)
- 1, 7, 89, 227, 623, 1589, 20203, 141421
- Prime factorisation
- 7 × 89 × 227
- Digit sum
- 13
- Digital root
- 4
Representations
- Decimal
- 141421
- Scientific notation
- 1.414 × 10^5
Roman numerals
Roman numerals as modelled here goes up to 3,999.
Binary
1 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1
1 × 131,072 + 0 × 65,536 + 0 × 32,768 + 0 × 16,384 + 1 × 8,192 + 0 × 4,096 + 1 × 2,048 + 0 × 1,024 + 0 × 512 + 0 × 256 + 0 × 128 + 1 × 64 + 1 × 32 + 0 × 16 + 1 × 8 + 1 × 4 + 0 × 2 + 1 × 1 = 141,421
Octal
4 2 4 1 5 5
4 × 32,768 + 2 × 4,096 + 4 × 512 + 1 × 64 + 5 × 8 + 5 × 1 = 141,421
Hexadecimal
2 2 8 6 d
2 × 65,536 + 2 × 4,096 + 8 × 256 + 6 × 16 + d × 1 = 141,421
Read as powers of two: 131,072 + 8,192 + 2,048 + 64 + 32 + 8 + 4 + 1 = 141,421.
In historical numeral systems
Egyptian
1 tadpole, 4 fingers, 1 lotus, 4 coils of rope, 2 hobbles, 1 stroke
1 × 100,000 + 4 × 10,000 + 1 × 1,000 + 4 × 100 + 2 × 10 + 1 × 1 = 141,421. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Systems that simply cannot reach this value are left out. Where a script needs a font most readers do not have, the reading is given instead of the glyphs — see number systems for each system in full.
Other mathematical patterns
- Deficient number
Related numbers & connections
141421 appears in Numbers in measurement, the topic covering numbers that carry a documented measurement fact.
Numbers Around Us
- appears inUnits and measurement
why?
Strength 0.50, confidence "high".
Science
The square root of two written as its first six digits is 141,421. Its irrationality was the first ever proved. It is also the ratio behind A-series paper: halving an A4 sheet along its long side gives two sheets of the same proportions, which works at this ratio and no other.
DocumentedScienceGeography: worldwide
Common questions
Is 141,421 a prime number?
No, 141,421 is not prime.
What are the factors of 141,421?
The factors of 141,421 are 1, 7, 89, 227, 623, 1589, 20203, 141421.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 1 reviewer-confirmed record, sourced and reviewed before publication.
Last reviewed: 15 July 2026