Number dictionary · Exact arithmetic
800: factors and number facts
eight hundred is an even number and is composite. Its 18 positive divisors form 9 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- eight hundred
- Roman numeral
- DCCC
- Prime factorization
- 2^5 × 5^2
- Digital root
- 8
All factors of 800
A positive factor divides 800 with no remainder. In ascending order, the complete list is:
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800
Factor pairs
- 1 × 800 = 800
- 2 × 400 = 800
- 4 × 200 = 800
- 5 × 160 = 800
- 8 × 100 = 800
- 10 × 80 = 800
- 16 × 50 = 800
- 20 × 40 = 800
- 25 × 32 = 800
Each pair describes an arrangement of 800 items into equal rows. The pairs have different row and column counts; 800 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 18
- Sum of all divisors
- 1953
- Sum excluding 800
- 1153
- Classification
- abundant
800 is abundant because its proper divisors add to 1153, which is greater than 800.
Prime factorization of 800
800 = 2^5 × 5^2
Repeated division, step by step
- 800 ÷ 2 = 400
- 400 ÷ 2 = 200
- 200 ÷ 2 = 100
- 100 ÷ 2 = 50
- 50 ÷ 2 = 25
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1
Multiply the prime divisors in these steps to reconstruct 800. An exponent records how many times the same prime occurs. The divisor-count calculation is (5 + 1) × (2 + 1) = 18.
The preceding prime is 797. The next larger prime is 809. The factor list above explains why 800 is composite.
Learn the factorization method800 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | eight hundred |
| Roman numeral | DCCC |
| Binary (base 2) | 1100100000 |
| Octal (base 8) | 1440 |
| Decimal (base 10) | 800 |
| Hexadecimal (base 16) | 320 |
Check the binary conversion
Read 1100100000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
512 + 256 + 32 = 800
Check the hexadecimal conversion
3 × 16^2 + 2 × 16^1 + 0 × 16^0 = 800
Hexadecimal uses A through F for digit values 10 through 15. These notations represent the same quantity; changing the base does not change the integer.
Square, cube and square root of 800
- 800 squared
- 800 × 800 = 640,000
- 800 cubed
- 800 × 800 × 800 = 512,000,000
- Square root
- ≈ 28.284271
- Simplified radical
- 20√2
800 lies between 784 (28²) and 841 (29²), so it is not a perfect square. It is not a perfect cube.
800 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 800.
Distinguish a square from a square rootMultiplication table for 800
These are the first twelve positive multiples. Unlike the finite factor list, the sequence of multiples continues without an upper limit.
Divisibility checks
| Divide by | Whole quotient | Remainder | Divides exactly? |
|---|---|---|---|
| 2 | 400 | 0 | Yes |
| 3 | 266 | 2 | No |
| 4 | 200 | 0 | Yes |
| 5 | 160 | 0 | Yes |
| 6 | 133 | 2 | No |
| 7 | 114 | 2 | No |
| 8 | 100 | 0 | Yes |
| 9 | 88 | 8 | No |
| 10 | 80 | 0 | Yes |
| 11 | 72 | 8 | No |
| 12 | 66 | 8 | No |
For example, 800 = 7 × 114 + 2. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 800
800 contains 3 decimal digits. Its digit sum is 8 + 0 + 0 = 8.
- 800: 8 + 0 + 0 = 8
The digital root is 8. Reversing its digits gives 008; it is not a decimal palindrome. Digit patterns depend on the notation being used.
Digital-root arithmetic always finishes at a single digit for a positive integer. Some numerology methods stop at 11, 22 or 33 instead; that is a separate interpretive convention.
Fractions and a worked comparison
As a fraction of 100, 800/100 simplifies to 8/1 by dividing both terms by their greatest common divisor, 100. Its decimal value is 8. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 800 and 12 is 4. Their least common multiple is 2400. The identity GCD × LCM = 800 × 12 = 9600 checks both results.
Work through GCF and LCMQuestions about 800
What are the factors of 800?
The positive factors are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800. There are 18 factors, including 1 and 800.
Is 800 a prime number?
No. 800 is composite: 2^5 × 5^2 = 800.
How do you write 800 in Roman numerals?
800 is DCCC in standard subtractive Roman numeral notation.
What is the binary representation of 800?
800 in decimal is 1100100000 in base 2. Adding its active place values gives 512 + 256 + 32 = 800.
Methods and reference definitions
Number JD calculates each result from the integer on this page. Positive factors are enumerated in pairs; repeated division gives the prime factorization; place values verify base conversions. Decimal square roots are rounded to six places when irrational.
NUMBER JOURNAL / JD
A reflective note on 800
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 800 add to 8. That arithmetic result is separate from the cultural symbolism of the pattern. If this number matters to you, write down what you noticed and choose one grounded action rather than treating the sighting as a prediction.