Number dictionary · Exact arithmetic
801: factors and number facts
eight hundred one is an odd number and is composite. Its 6 positive divisors form 3 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- eight hundred one
- Roman numeral
- DCCCI
- Prime factorization
- 3^2 × 89
- Digital root
- 9
All factors of 801
A positive factor divides 801 with no remainder. In ascending order, the complete list is:
1, 3, 9, 89, 267, 801
Factor pairs
- 1 × 801 = 801
- 3 × 267 = 801
- 9 × 89 = 801
Each pair describes an arrangement of 801 items into equal rows. The pairs have different row and column counts; 801 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 6
- Sum of all divisors
- 1170
- Sum excluding 801
- 369
- Classification
- deficient
801 is deficient because its proper divisors add to 369, which is less than 801.
Prime factorization of 801
801 = 3^2 × 89
Repeated division, step by step
- 801 ÷ 3 = 267
- 267 ÷ 3 = 89
- 89 ÷ 89 = 1
Multiply the prime divisors in these steps to reconstruct 801. An exponent records how many times the same prime occurs. The divisor-count calculation is (2 + 1) × (1 + 1) = 6.
The preceding prime is 797. The next larger prime is 809. The factor list above explains why 801 is composite.
Learn the factorization method801 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | eight hundred one |
| Roman numeral | DCCCI |
| Binary (base 2) | 1100100001 |
| Octal (base 8) | 1441 |
| Decimal (base 10) | 801 |
| Hexadecimal (base 16) | 321 |
Check the binary conversion
Read 1100100001 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 + 1 = 801
Check the hexadecimal conversion
3 × 16^2 + 2 × 16^1 + 1 × 16^0 = 801
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 801
- 801 squared
- 801 × 801 = 641,601
- 801 cubed
- 801 × 801 × 801 = 513,922,401
- Square root
- ≈ 28.301943
- Simplified radical
- 3√89
801 lies between 784 (28²) and 841 (29²), so it is not a perfect square. It is not a perfect cube.
801 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 801.
Distinguish a square from a square rootMultiplication table for 801
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 | 1 | No |
| 3 | 267 | 0 | Yes |
| 4 | 200 | 1 | No |
| 5 | 160 | 1 | No |
| 6 | 133 | 3 | No |
| 7 | 114 | 3 | No |
| 8 | 100 | 1 | No |
| 9 | 89 | 0 | Yes |
| 10 | 80 | 1 | No |
| 11 | 72 | 9 | No |
| 12 | 66 | 9 | No |
For example, 801 = 7 × 114 + 3. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 801
801 contains 3 decimal digits. Its digit sum is 8 + 0 + 1 = 9.
- 801: 8 + 0 + 1 = 9
The digital root is 9. Reversing its digits gives 108; 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, 801/100 simplifies to 801/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 8.01. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 801 and 12 is 3. Their least common multiple is 3204. The identity GCD × LCM = 801 × 12 = 9612 checks both results.
Work through GCF and LCMQuestions about 801
What are the factors of 801?
The positive factors are 1, 3, 9, 89, 267, 801. There are 6 factors, including 1 and 801.
Is 801 a prime number?
No. 801 is composite: 3^2 × 89 = 801.
How do you write 801 in Roman numerals?
801 is DCCCI in standard subtractive Roman numeral notation.
What is the binary representation of 801?
801 in decimal is 1100100001 in base 2. Adding its active place values gives 512 + 256 + 32 + 1 = 801.
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 801
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 801 add to 9. 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.