Number reference
800 explained.
800: eight hundred, composite; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- eight hundred
- Classification
- composite
- Factors
- 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800
- Prime factorization
- 2 × 2 × 2 × 2 × 2 × 5 × 5
- Square root
- 28.284271
- Cube root
- 9.283178
- Binary
- 1100100000
- Octal
- 1440
- Hexadecimal
- 320
- Roman numeral
- DCCC
- Digit sum
- 8
- Digital root
- 8
What makes 800 notable
- Factor structure. 800 breaks down into 2 distinct primes (2, 5) and has 18 divisors in total, so it can be split into equal whole-number groups 16 ways beyond 1 and itself.
800 in everyday use
Eight hundred is the toll-free prefix. AT&T introduced 1-800 numbers in the United States in 1967, and the digits became so tied to free calling that "an 800 number" still means a customer-service line even though 888, 877, and other prefixes now do the same job. In athletics the 800 metres is two laps of the track, the shortest middle-distance event. In Roman numerals it is DCCC, and 800 is the maximum score on each section of the SAT.
Factored, 800 is 2⁵ × 5², with eighteen divisors, and it is twice a square, 2 × 20². It is a sum of two squares in two ways: 20² + 20² = 400 + 400 and 28² + 4² = 784 + 16. It is 1100100000 in binary and 320 in hexadecimal. Its digit sum is 8, which divides it, so it is a Harshad number, and it lies between the primes 797 and 809.
Nearby numbers
How to read this page
The factor list shows every way 800 splits into equal whole-number groups — 18 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 800 for contexts that do not use decimal.
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