407
407 is the largest three-digit narcissistic number (4³ + 0³ + 7³ = 407), and the HTTP status code for 'Proxy Authentication Required'.
- Odd
- Composite
Where 407 fits
Why 407 is special
407 closes the three-digit narcissistic sequence — no larger three-digit number equals the sum of the cubes of its own digits. It also has a second, entirely unrelated life as an HTTP status code: 407 tells a client it must authenticate with a proxy before the request can proceed.
Not just a mathematical number
407is also used in ways where ordinary arithmetic doesn't apply — each listed below with what genuinely does and doesn't follow from it.
- Mathematical number
A genuine quantity — its mathematical properties (prime, square, factors, and so on) are real facts about it.
A genuine quantity that ordinary arithmetic applies to — it can be prime, even, a perfect square, added to another number meaningfully, and so on.
- Code
Also used as a code — HTTP status codes.
An assigned identifier from a fixed registry or standard — its digits don't represent an amount, and arithmetic on it is meaningless (HTTP status 404 + 1 is not a 'better' status; it's a different, unrelated code).
Factors & digit properties
- Divisors (4)
- 1, 11, 37, 407
- Prime factorisation
- 11 × 37
- Digit sum
- 11
- Digital root
- 2
Representations
- Decimal
- 407
- Scientific notation
- 4.070 × 10^2
Roman numerals
C D V I I
CDVII uses the subtractive pair CD: a hundred before five hundred — five hundred minus a hundred.
Binary
1 1 0 0 1 0 1 1 1
1 × 256 + 1 × 128 + 0 × 64 + 0 × 32 + 1 × 16 + 0 × 8 + 1 × 4 + 1 × 2 + 1 × 1 = 407
Octal
6 2 7
6 × 64 + 2 × 8 + 7 × 1 = 407
Hexadecimal
1 9 7
1 × 256 + 9 × 16 + 7 × 1 = 407
Read as powers of two: 256 + 128 + 16 + 4 + 2 + 1 = 407.
In historical numeral systems
Egyptian
4 coils of rope, 7 strokes
4 × 100 + 7 × 1 = 407. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
6 vertical wedges (sixties place), 4 corner wedges + 7 vertical wedges (units place)
6 × 60 + 47 = 407. Places are separated by a space on the tablet, with the higher place written first.
Greek (Ionic)
upsilon, then zeta, marked as a numeral
upsilon-zeta + keraia
upsilon + zeta written in descending order and added — the letters carry their values wherever they stand, so this is addition, not place value.
Hebrew numerals
tav, then zayin
tav-zayin
tav (400) + zayin (7) = 407, written in descending order.
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
- Narcissistic (Armstrong) number
- Semiprime
- Harshad (Niven) number
Related numbers & connections
407 is the semiprime 11 × 37, so it is a multiple of 11.
View 11 →HTTP status code 407 ('Proxy Authentication Required') is formally defined in RFC 9110: the client must authenticate with a proxy before the request can be fulfilled.
Technology & computing
HTTP status code 407 ('Proxy Authentication Required') is formally defined in IETF specifications (now RFC 9110) to indicate that the client must first authenticate itself with a proxy before the request can be fulfilled.
DocumentedTechnology & computing
Mathematics
407 is the largest three-digit narcissistic (Armstrong) number: 4³ + 0³ + 7³ = 64 + 0 + 343 = 407. It factors as the semiprime 11 × 37.
DocumentedMathematics
Common questions
Is 407 a prime number?
No, 407 is not prime.
What are the factors of 407?
The factors of 407 are 1, 11, 37, 407.
What is 407 in Roman numerals?
407 in Roman numerals is CDVII. CD is subtractive: a hundred before five hundred — five hundred minus a hundred. Written additively it would be CCCCVII, which Roman inscriptions used freely — the strict subtractive form is a later convention.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 2 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026