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.
Factors & digit properties
- Divisors (4)
- 1, 11, 37, 407
- Prime factorisation
- 11 × 37
- Digit sum
- 11
- Digital root
- 2
Representations
- Decimal
- 407
- Binary
- 110010111
- Octal
- 627
- Hexadecimal
- 197
- Roman numeral
- CDVII
- Scientific notation
- 4.070 × 10^2
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 →Mathematically related
- is a multiple of11
why?
Strength 0.50, confidence "high".
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.
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: 30 July 2026