Number dictionary · Exact arithmetic
864: factors and number facts
eight hundred sixty-four is an even number and is composite. Its 24 positive divisors form 12 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- eight hundred sixty-four
- Roman numeral
- DCCCLXIV
- Prime factorization
- 2^5 × 3^3
- Digital root
- 9
All factors of 864
A positive factor divides 864 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
Factor pairs
- 1 × 864 = 864
- 2 × 432 = 864
- 3 × 288 = 864
- 4 × 216 = 864
- 6 × 144 = 864
- 8 × 108 = 864
- 9 × 96 = 864
- 12 × 72 = 864
- 16 × 54 = 864
- 18 × 48 = 864
- 24 × 36 = 864
- 27 × 32 = 864
Each pair describes an arrangement of 864 items into equal rows. The pairs have different row and column counts; 864 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 24
- Sum of all divisors
- 2520
- Sum excluding 864
- 1656
- Classification
- abundant
864 is abundant because its proper divisors add to 1656, which is greater than 864.
Prime factorization of 864
864 = 2^5 × 3^3
Repeated division, step by step
- 864 ÷ 2 = 432
- 432 ÷ 2 = 216
- 216 ÷ 2 = 108
- 108 ÷ 2 = 54
- 54 ÷ 2 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1
Multiply the prime divisors in these steps to reconstruct 864. An exponent records how many times the same prime occurs. The divisor-count calculation is (5 + 1) × (3 + 1) = 24.
The preceding prime is 863. The next larger prime is 877. The factor list above explains why 864 is composite.
Learn the factorization method864 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | eight hundred sixty-four |
| Roman numeral | DCCCLXIV |
| Binary (base 2) | 1101100000 |
| Octal (base 8) | 1540 |
| Decimal (base 10) | 864 |
| Hexadecimal (base 16) | 360 |
Check the binary conversion
Read 1101100000 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 + 64 + 32 = 864
Check the hexadecimal conversion
3 × 16^2 + 6 × 16^1 + 0 × 16^0 = 864
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 864
- 864 squared
- 864 × 864 = 746,496
- 864 cubed
- 864 × 864 × 864 = 644,972,544
- Square root
- ≈ 29.393877
- Simplified radical
- 12√6
864 lies between 841 (29²) and 900 (30²), so it is not a perfect square. It is not a perfect cube.
864 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 864.
Distinguish a square from a square rootMultiplication table for 864
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 | 432 | 0 | Yes |
| 3 | 288 | 0 | Yes |
| 4 | 216 | 0 | Yes |
| 5 | 172 | 4 | No |
| 6 | 144 | 0 | Yes |
| 7 | 123 | 3 | No |
| 8 | 108 | 0 | Yes |
| 9 | 96 | 0 | Yes |
| 10 | 86 | 4 | No |
| 11 | 78 | 6 | No |
| 12 | 72 | 0 | Yes |
For example, 864 = 7 × 123 + 3. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 864
864 contains 3 decimal digits. Its digit sum is 8 + 6 + 4 = 18.
- 864: 8 + 6 + 4 = 18
- 18: 1 + 8 = 9
The digital root is 9. Reversing its digits gives 468; 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, 864/100 simplifies to 216/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 8.64. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 864 and 12 is 12. Their least common multiple is 864. The identity GCD × LCM = 864 × 12 = 10368 checks both results.
Work through GCF and LCMQuestions about 864
What are the factors of 864?
The positive factors are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864. There are 24 factors, including 1 and 864.
Is 864 a prime number?
No. 864 is composite: 2^5 × 3^3 = 864.
How do you write 864 in Roman numerals?
864 is DCCCLXIV in standard subtractive Roman numeral notation.
What is the binary representation of 864?
864 in decimal is 1101100000 in base 2. Adding its active place values gives 512 + 256 + 64 + 32 = 864.
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 864
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 864 add to 18. 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.