Number dictionary · Exact arithmetic
767: factors and number facts
seven 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
- seven hundred sixty-seven
- Roman numeral
- DCCLXVII
- Prime factorization
- 13 × 59
- Digital root
- 2
All factors of 767
A positive factor divides 767 with no remainder. In ascending order, the complete list is:
1, 13, 59, 767
Factor pairs
- 1 × 767 = 767
- 13 × 59 = 767
Each pair describes an arrangement of 767 items into equal rows. The pairs have different row and column counts; 767 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 4
- Sum of all divisors
- 840
- Sum excluding 767
- 73
- Classification
- deficient
767 is deficient because its proper divisors add to 73, which is less than 767.
Prime factorization of 767
767 = 13 × 59
Repeated division, step by step
- 767 ÷ 13 = 59
- 59 ÷ 59 = 1
Multiply the prime divisors in these steps to reconstruct 767. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) = 4.
The preceding prime is 761. The next larger prime is 769. The factor list above explains why 767 is composite.
Learn the factorization method767 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | seven hundred sixty-seven |
| Roman numeral | DCCLXVII |
| Binary (base 2) | 1011111111 |
| Octal (base 8) | 1377 |
| Decimal (base 10) | 767 |
| Hexadecimal (base 16) | 2FF |
Check the binary conversion
Read 1011111111 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
512 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 767
Check the hexadecimal conversion
2 × 16^2 + 15 × 16^1 + 15 × 16^0 = 767
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 767
- 767 squared
- 767 × 767 = 588,289
- 767 cubed
- 767 × 767 × 767 = 451,217,663
- Square root
- ≈ 27.694765
- Simplified radical
- √767
767 lies between 729 (27²) and 784 (28²), so it is not a perfect square. It is not a perfect cube.
767 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 767.
Distinguish a square from a square rootMultiplication table for 767
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 | 383 | 1 | No |
| 3 | 255 | 2 | No |
| 4 | 191 | 3 | No |
| 5 | 153 | 2 | No |
| 6 | 127 | 5 | No |
| 7 | 109 | 4 | No |
| 8 | 95 | 7 | No |
| 9 | 85 | 2 | No |
| 10 | 76 | 7 | No |
| 11 | 69 | 8 | No |
| 12 | 63 | 11 | No |
For example, 767 = 7 × 109 + 4. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 767
767 contains 3 decimal digits. Its digit sum is 7 + 6 + 7 = 20.
- 767: 7 + 6 + 7 = 20
- 20: 2 + 0 = 2
The digital root is 2. 767 reads the same forward and backward, making it 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, 767/100 simplifies to 767/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 7.67. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 767 and 12 is 1. Their least common multiple is 9204. The identity GCD × LCM = 767 × 12 = 9204 checks both results.
Work through GCF and LCMQuestions about 767
What are the factors of 767?
The positive factors are 1, 13, 59, 767. There are 4 factors, including 1 and 767.
Is 767 a prime number?
No. 767 is composite: 13 × 59 = 767.
How do you write 767 in Roman numerals?
767 is DCCLXVII in standard subtractive Roman numeral notation.
What is the binary representation of 767?
767 in decimal is 1011111111 in base 2. Adding its active place values gives 512 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 767.
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 767
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 767 add to 20. 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.