Number dictionary · Exact arithmetic
267: factors and number facts
two hundred sixty-seven is an odd number and is composite. Its 4 positive divisors form 2 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- two hundred sixty-seven
- Roman numeral
- CCLXVII
- Prime factorization
- 3 × 89
- Digital root
- 6
All factors of 267
A positive factor divides 267 with no remainder. In ascending order, the complete list is:
1, 3, 89, 267
Factor pairs
- 1 × 267 = 267
- 3 × 89 = 267
Each pair describes an arrangement of 267 items into equal rows. The pairs have different row and column counts; 267 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 4
- Sum of all divisors
- 360
- Sum excluding 267
- 93
- Classification
- deficient
267 is deficient because its proper divisors add to 93, which is less than 267.
Prime factorization of 267
267 = 3 × 89
Repeated division, step by step
- 267 ÷ 3 = 89
- 89 ÷ 89 = 1
Multiply the prime divisors in these steps to reconstruct 267. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) = 4.
The preceding prime is 263. The next larger prime is 269. The factor list above explains why 267 is composite.
Learn the factorization method267 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | two hundred sixty-seven |
| Roman numeral | CCLXVII |
| Binary (base 2) | 100001011 |
| Octal (base 8) | 413 |
| Decimal (base 10) | 267 |
| Hexadecimal (base 16) | 10B |
Check the binary conversion
Read 100001011 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 + 2 + 1 = 267
Check the hexadecimal conversion
1 × 16^2 + 0 × 16^1 + 11 × 16^0 = 267
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 267
- 267 squared
- 267 × 267 = 71,289
- 267 cubed
- 267 × 267 × 267 = 19,034,163
- Square root
- ≈ 16.340135
- Simplified radical
- √267
267 lies between 256 (16²) and 289 (17²), so it is not a perfect square. It is not a perfect cube.
267 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 267.
Distinguish a square from a square rootMultiplication table for 267
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 | 133 | 1 | No |
| 3 | 89 | 0 | Yes |
| 4 | 66 | 3 | No |
| 5 | 53 | 2 | No |
| 6 | 44 | 3 | No |
| 7 | 38 | 1 | No |
| 8 | 33 | 3 | No |
| 9 | 29 | 6 | No |
| 10 | 26 | 7 | No |
| 11 | 24 | 3 | No |
| 12 | 22 | 3 | No |
For example, 267 = 7 × 38 + 1. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 267
267 contains 3 decimal digits. Its digit sum is 2 + 6 + 7 = 15.
- 267: 2 + 6 + 7 = 15
- 15: 1 + 5 = 6
The digital root is 6. Reversing its digits gives 762; 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, 267/100 simplifies to 267/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 2.67. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 267 and 12 is 3. Their least common multiple is 1068. The identity GCD × LCM = 267 × 12 = 3204 checks both results.
Work through GCF and LCMQuestions about 267
What are the factors of 267?
The positive factors are 1, 3, 89, 267. There are 4 factors, including 1 and 267.
Is 267 a prime number?
No. 267 is composite: 3 × 89 = 267.
How do you write 267 in Roman numerals?
267 is CCLXVII in standard subtractive Roman numeral notation.
What is the binary representation of 267?
267 in decimal is 100001011 in base 2. Adding its active place values gives 256 + 8 + 2 + 1 = 267.
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 267
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 267 add to 15. 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.