313
313 is the year the Edict of Milan legalised Christianity in the Roman Empire.
- Odd
- Prime
Where 313 fits
Why 313 is special
It granted toleration to all religions rather than privileging Christianity, which came later. The distinction is routinely collapsed in accounts that treat 313 as the conversion of the empire.
Factors & digit properties
- Divisors (2)
- 1, 313
- Prime factorisation
- 313
- Digit sum
- 7
- Digital root
- 7
Representations
- Decimal
- 313
- Scientific notation
- 3.130 × 10^2
Roman numerals
C C C X I I I
Binary
1 0 0 1 1 1 0 0 1
1 × 256 + 0 × 128 + 0 × 64 + 1 × 32 + 1 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 313
Octal
4 7 1
4 × 64 + 7 × 8 + 1 × 1 = 313
Hexadecimal
1 3 9
1 × 256 + 3 × 16 + 9 × 1 = 313
Read as powers of two: 256 + 32 + 16 + 8 + 1 = 313.
In historical numeral systems
Egyptian
3 coils of rope, 1 hobble, 3 strokes
3 × 100 + 1 × 10 + 3 × 1 = 313. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
5 vertical wedges (sixties place), 1 corner wedge + 3 vertical wedges (units place)
5 × 60 + 13 = 313. Places are separated by a space on the tablet, with the higher place written first.
Greek (Ionic)
tau, then iota, then gamma, marked as a numeral
tau-iota-gamma + keraia
tau + iota + gamma written in descending order and added — the letters carry their values wherever they stand, so this is addition, not place value.
Hebrew numerals
shin, then yod, then gimel
shin-yod-gimel
shin (300) + yod (10) + gimel (3) = 313, written in descending order.
Maya
3 bars (upper, twenties place) over 2 bars + 3 dots (lower, units place)
15 × 20 + 13 = 313. Places stack vertically with the smallest at the bottom, so the upper group is worth twenty times the lower.
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
- Palindromic number
- Deficient number
- Happy number
- Twin prime
Law & regulation
The Edict of Milan extended legal protection to all cults, Christianity included. Christianity became the state religion in 380, and conflating the two dates misstates what changed in 313.
DocumentedLaw & regulationGeography: Roman EmpirePeriod: 313
Common questions
Is 313 a prime number?
Yes, 313 is prime — it has exactly two positive divisors: 1 and itself.
What are the factors of 313?
The factors of 313 are 1, 313.
What is 313 in Roman numerals?
313 in Roman numerals is CCCXIII.
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