Number dictionary · Exact arithmetic
967: factors and number facts
nine hundred sixty-seven is an odd number and is prime. Its 2 positive divisors form 1 factor pair.
Number JD Editorial Team · Updated 2026-10-08
- In words
- nine hundred sixty-seven
- Roman numeral
- CMLXVII
- Prime factorization
- 967
- Digital root
- 4
All factors of 967
A positive factor divides 967 with no remainder. In ascending order, the complete list is:
1, 967
Factor pairs
- 1 × 967 = 967
Each pair describes an arrangement of 967 items into equal rows. The pairs have different row and column counts; 967 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 2
- Sum of all divisors
- 968
- Sum excluding 967
- 1
- Classification
- deficient
967 is deficient because its proper divisors add to 1, which is less than 967.
Prime factorization of 967
967 = 967
Repeated division, step by step
- 967 ÷ 967 = 1
Multiply the prime divisors in these steps to reconstruct 967. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) = 2.
The preceding prime is 953. The next larger prime is 971. To check 967 for primality, it is sufficient to test possible divisors from 2 through 31.
Learn the factorization method967 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | nine hundred sixty-seven |
| Roman numeral | CMLXVII |
| Binary (base 2) | 1111000111 |
| Octal (base 8) | 1707 |
| Decimal (base 10) | 967 |
| Hexadecimal (base 16) | 3C7 |
Check the binary conversion
Read 1111000111 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 + 128 + 64 + 4 + 2 + 1 = 967
Check the hexadecimal conversion
3 × 16^2 + 12 × 16^1 + 7 × 16^0 = 967
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 967
- 967 squared
- 967 × 967 = 935,089
- 967 cubed
- 967 × 967 × 967 = 904,231,063
- Square root
- ≈ 31.096624
- Simplified radical
- √967
967 lies between 961 (31²) and 1024 (32²), so it is not a perfect square. It is not a perfect cube.
967 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 967.
Distinguish a square from a square rootMultiplication table for 967
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 | 483 | 1 | No |
| 3 | 322 | 1 | No |
| 4 | 241 | 3 | No |
| 5 | 193 | 2 | No |
| 6 | 161 | 1 | No |
| 7 | 138 | 1 | No |
| 8 | 120 | 7 | No |
| 9 | 107 | 4 | No |
| 10 | 96 | 7 | No |
| 11 | 87 | 10 | No |
| 12 | 80 | 7 | No |
For example, 967 = 7 × 138 + 1. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 967
967 contains 3 decimal digits. Its digit sum is 9 + 6 + 7 = 22.
- 967: 9 + 6 + 7 = 22
- 22: 2 + 2 = 4
The digital root is 4. Reversing its digits gives 769; 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, 967/100 simplifies to 967/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 9.67. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 967 and 12 is 1. Their least common multiple is 11604. The identity GCD × LCM = 967 × 12 = 11604 checks both results.
Work through GCF and LCMQuestions about 967
What are the factors of 967?
The positive factors are 1, 967. There are 2 factors, including 1 and 967.
Is 967 a prime number?
Yes. The only positive divisors of 967 are 1 and 967.
How do you write 967 in Roman numerals?
967 is CMLXVII in standard subtractive Roman numeral notation.
What is the binary representation of 967?
967 in decimal is 1111000111 in base 2. Adding its active place values gives 512 + 256 + 128 + 64 + 4 + 2 + 1 = 967.
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 967
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 967 add to 22. 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.