Number dictionary · Exact arithmetic
67: factors and number facts
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
- sixty-seven
- Roman numeral
- LXVII
- Prime factorization
- 67
- Digital root
- 4
All factors of 67
A positive factor divides 67 with no remainder. In ascending order, the complete list is:
1, 67
Factor pairs
- 1 × 67 = 67
Each pair describes an arrangement of 67 items into equal rows. The pairs have different row and column counts; 67 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 2
- Sum of all divisors
- 68
- Sum excluding 67
- 1
- Classification
- deficient
67 is deficient because its proper divisors add to 1, which is less than 67.
Prime factorization of 67
67 = 67
Repeated division, step by step
- 67 ÷ 67 = 1
Multiply the prime divisors in these steps to reconstruct 67. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) = 2.
The preceding prime is 61. The next larger prime is 71. To check 67 for primality, it is sufficient to test possible divisors from 2 through 8.
Learn the factorization method67 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | sixty-seven |
| Roman numeral | LXVII |
| Binary (base 2) | 1000011 |
| Octal (base 8) | 103 |
| Decimal (base 10) | 67 |
| Hexadecimal (base 16) | 43 |
Check the binary conversion
Read 1000011 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
64 + 2 + 1 = 67
Check the hexadecimal conversion
4 × 16^1 + 3 × 16^0 = 67
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 67
- 67 squared
- 67 × 67 = 4,489
- 67 cubed
- 67 × 67 × 67 = 300,763
- Square root
- ≈ 8.185353
- Simplified radical
- √67
67 lies between 64 (8²) and 81 (9²), so it is not a perfect square. It is not a perfect cube.
67 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 67.
Distinguish a square from a square rootMultiplication table for 67
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 | 33 | 1 | No |
| 3 | 22 | 1 | No |
| 4 | 16 | 3 | No |
| 5 | 13 | 2 | No |
| 6 | 11 | 1 | No |
| 7 | 9 | 4 | No |
| 8 | 8 | 3 | No |
| 9 | 7 | 4 | No |
| 10 | 6 | 7 | No |
| 11 | 6 | 1 | No |
| 12 | 5 | 7 | No |
For example, 67 = 7 × 9 + 4. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 67
67 contains 2 decimal digits. Its digit sum is 6 + 7 = 13.
- 67: 6 + 7 = 13
- 13: 1 + 3 = 4
The digital root is 4. Reversing its digits gives 76; 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, 67/100 simplifies to 67/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 0.67.
The greatest common divisor of 67 and 12 is 1. Their least common multiple is 804. The identity GCD × LCM = 67 × 12 = 804 checks both results.
Work through GCF and LCMQuestions about 67
What are the factors of 67?
The positive factors are 1, 67. There are 2 factors, including 1 and 67.
Is 67 a prime number?
Yes. The only positive divisors of 67 are 1 and 67.
How do you write 67 in Roman numerals?
67 is LXVII in standard subtractive Roman numeral notation.
What is the binary representation of 67?
67 in decimal is 1000011 in base 2. Adding its active place values gives 64 + 2 + 1 = 67.
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 67
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 67 add to 13. 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.