Number dictionary · Exact arithmetic
367: factors and number facts
three 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
- three hundred sixty-seven
- Roman numeral
- CCCLXVII
- Prime factorization
- 367
- Digital root
- 7
All factors of 367
A positive factor divides 367 with no remainder. In ascending order, the complete list is:
1, 367
Factor pairs
- 1 × 367 = 367
Each pair describes an arrangement of 367 items into equal rows. The pairs have different row and column counts; 367 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 2
- Sum of all divisors
- 368
- Sum excluding 367
- 1
- Classification
- deficient
367 is deficient because its proper divisors add to 1, which is less than 367.
Prime factorization of 367
367 = 367
Repeated division, step by step
- 367 ÷ 367 = 1
Multiply the prime divisors in these steps to reconstruct 367. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) = 2.
The preceding prime is 359. The next larger prime is 373. To check 367 for primality, it is sufficient to test possible divisors from 2 through 19.
Learn the factorization method367 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred sixty-seven |
| Roman numeral | CCCLXVII |
| Binary (base 2) | 101101111 |
| Octal (base 8) | 557 |
| Decimal (base 10) | 367 |
| Hexadecimal (base 16) | 16F |
Check the binary conversion
Read 101101111 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
256 + 64 + 32 + 8 + 4 + 2 + 1 = 367
Check the hexadecimal conversion
1 × 16^2 + 6 × 16^1 + 15 × 16^0 = 367
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 367
- 367 squared
- 367 × 367 = 134,689
- 367 cubed
- 367 × 367 × 367 = 49,430,863
- Square root
- ≈ 19.157244
- Simplified radical
- √367
367 lies between 361 (19²) and 400 (20²), so it is not a perfect square. It is not a perfect cube.
367 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 367.
Distinguish a square from a square rootMultiplication table for 367
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 | 183 | 1 | No |
| 3 | 122 | 1 | No |
| 4 | 91 | 3 | No |
| 5 | 73 | 2 | No |
| 6 | 61 | 1 | No |
| 7 | 52 | 3 | No |
| 8 | 45 | 7 | No |
| 9 | 40 | 7 | No |
| 10 | 36 | 7 | No |
| 11 | 33 | 4 | No |
| 12 | 30 | 7 | No |
For example, 367 = 7 × 52 + 3. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 367
367 contains 3 decimal digits. Its digit sum is 3 + 6 + 7 = 16.
- 367: 3 + 6 + 7 = 16
- 16: 1 + 6 = 7
The digital root is 7. Reversing its digits gives 763; 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, 367/100 simplifies to 367/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 3.67. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 367 and 12 is 1. Their least common multiple is 4404. The identity GCD × LCM = 367 × 12 = 4404 checks both results.
Work through GCF and LCMQuestions about 367
What are the factors of 367?
The positive factors are 1, 367. There are 2 factors, including 1 and 367.
Is 367 a prime number?
Yes. The only positive divisors of 367 are 1 and 367.
How do you write 367 in Roman numerals?
367 is CCCLXVII in standard subtractive Roman numeral notation.
What is the binary representation of 367?
367 in decimal is 101101111 in base 2. Adding its active place values gives 256 + 64 + 32 + 8 + 4 + 2 + 1 = 367.
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 367
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 367 add to 16. 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.