Number dictionary · Exact arithmetic
264: factors and number facts
two hundred sixty-four is an even number and is composite. Its 16 positive divisors form 8 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- two hundred sixty-four
- Roman numeral
- CCLXIV
- Prime factorization
- 2^3 × 3 × 11
- Digital root
- 3
All factors of 264
A positive factor divides 264 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264
Factor pairs
- 1 × 264 = 264
- 2 × 132 = 264
- 3 × 88 = 264
- 4 × 66 = 264
- 6 × 44 = 264
- 8 × 33 = 264
- 11 × 24 = 264
- 12 × 22 = 264
Each pair describes an arrangement of 264 items into equal rows. The pairs have different row and column counts; 264 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 16
- Sum of all divisors
- 720
- Sum excluding 264
- 456
- Classification
- abundant
264 is abundant because its proper divisors add to 456, which is greater than 264.
Prime factorization of 264
264 = 2^3 × 3 × 11
Repeated division, step by step
- 264 ÷ 2 = 132
- 132 ÷ 2 = 66
- 66 ÷ 2 = 33
- 33 ÷ 3 = 11
- 11 ÷ 11 = 1
Multiply the prime divisors in these steps to reconstruct 264. An exponent records how many times the same prime occurs. The divisor-count calculation is (3 + 1) × (1 + 1) × (1 + 1) = 16.
The preceding prime is 263. The next larger prime is 269. The factor list above explains why 264 is composite.
Learn the factorization method264 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | two hundred sixty-four |
| Roman numeral | CCLXIV |
| Binary (base 2) | 100001000 |
| Octal (base 8) | 410 |
| Decimal (base 10) | 264 |
| Hexadecimal (base 16) | 108 |
Check the binary conversion
Read 100001000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
256 + 8 = 264
Check the hexadecimal conversion
1 × 16^2 + 0 × 16^1 + 8 × 16^0 = 264
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 264
- 264 squared
- 264 × 264 = 69,696
- 264 cubed
- 264 × 264 × 264 = 18,399,744
- Square root
- ≈ 16.248077
- Simplified radical
- 2√66
264 lies between 256 (16²) and 289 (17²), so it is not a perfect square. It is not a perfect cube.
264 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 264.
Distinguish a square from a square rootMultiplication table for 264
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 | 132 | 0 | Yes |
| 3 | 88 | 0 | Yes |
| 4 | 66 | 0 | Yes |
| 5 | 52 | 4 | No |
| 6 | 44 | 0 | Yes |
| 7 | 37 | 5 | No |
| 8 | 33 | 0 | Yes |
| 9 | 29 | 3 | No |
| 10 | 26 | 4 | No |
| 11 | 24 | 0 | Yes |
| 12 | 22 | 0 | Yes |
For example, 264 = 7 × 37 + 5. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 264
264 contains 3 decimal digits. Its digit sum is 2 + 6 + 4 = 12.
- 264: 2 + 6 + 4 = 12
- 12: 1 + 2 = 3
The digital root is 3. Reversing its digits gives 462; 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, 264/100 simplifies to 66/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 2.64. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 264 and 12 is 12. Their least common multiple is 264. The identity GCD × LCM = 264 × 12 = 3168 checks both results.
Work through GCF and LCMQuestions about 264
What are the factors of 264?
The positive factors are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264. There are 16 factors, including 1 and 264.
Is 264 a prime number?
No. 264 is composite: 2^3 × 3 × 11 = 264.
How do you write 264 in Roman numerals?
264 is CCLXIV in standard subtractive Roman numeral notation.
What is the binary representation of 264?
264 in decimal is 100001000 in base 2. Adding its active place values gives 256 + 8 = 264.
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 264
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 264 add to 12. 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.