Number reference
400 explained.
400: four hundred, composite, perfect square; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- four hundred
- Classification
- composite
- Factors
- 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
- Prime factorization
- 2 × 2 × 2 × 2 × 5 × 5
- Square root
- 20
- Cube root
- 7.368063
- Binary
- 110010000
- Octal
- 620
- Hexadecimal
- 190
- Roman numeral
- CD
- Digit sum
- 4
- Digital root
- 4
What makes 400 notable
- Perfect square. 400 = 20², so a square of side 20 has an area of 400.
400 in everyday use
Four hundred is the length of the Gregorian calendar's cycle. Years divisible by 100 are not leap years unless they are also divisible by 400, which is why 2000 was a leap year and 1900 was not, and the whole pattern of weekdays repeats every 400 years, a span of exactly 146,097 days. The number also marks one lap of a standard athletics track, the 400-metre race, and it is the HTTP status for a bad request, the first of the 4xx client-error codes. In Roman numerals it is CD.
It is twenty squared, and factors as 2⁴ × 5², with fifteen divisors. Being a square it is the sum of the first twenty odd numbers, and it is also 12² + 16², a scaled 3-4-5 triangle. The 400-year cycle contains 97 leap years, since 400 × 365 + 97 = 146,097, and that total divides evenly by 7 into 20,871 weeks. Its digit sum is 4, and it is 110010000 in binary.
Nearby numbers
How to read this page
The factor list shows every way 400 splits into equal whole-number groups — 15 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 400 for contexts that do not use decimal.
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