Number dictionary · Exact arithmetic
364: factors and number facts
three hundred sixty-four is an even number and is composite. Its 12 positive divisors form 6 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- three hundred sixty-four
- Roman numeral
- CCCLXIV
- Prime factorization
- 2^2 × 7 × 13
- Digital root
- 4
All factors of 364
A positive factor divides 364 with no remainder. In ascending order, the complete list is:
1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364
Factor pairs
- 1 × 364 = 364
- 2 × 182 = 364
- 4 × 91 = 364
- 7 × 52 = 364
- 13 × 28 = 364
- 14 × 26 = 364
Each pair describes an arrangement of 364 items into equal rows. The pairs have different row and column counts; 364 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 12
- Sum of all divisors
- 784
- Sum excluding 364
- 420
- Classification
- abundant
364 is abundant because its proper divisors add to 420, which is greater than 364.
Prime factorization of 364
364 = 2^2 × 7 × 13
Repeated division, step by step
- 364 ÷ 2 = 182
- 182 ÷ 2 = 91
- 91 ÷ 7 = 13
- 13 ÷ 13 = 1
Multiply the prime divisors in these steps to reconstruct 364. An exponent records how many times the same prime occurs. The divisor-count calculation is (2 + 1) × (1 + 1) × (1 + 1) = 12.
The preceding prime is 359. The next larger prime is 367. The factor list above explains why 364 is composite.
Learn the factorization method364 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred sixty-four |
| Roman numeral | CCCLXIV |
| Binary (base 2) | 101101100 |
| Octal (base 8) | 554 |
| Decimal (base 10) | 364 |
| Hexadecimal (base 16) | 16C |
Check the binary conversion
Read 101101100 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 = 364
Check the hexadecimal conversion
1 × 16^2 + 6 × 16^1 + 12 × 16^0 = 364
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 364
- 364 squared
- 364 × 364 = 132,496
- 364 cubed
- 364 × 364 × 364 = 48,228,544
- Square root
- ≈ 19.078784
- Simplified radical
- 2√91
364 lies between 361 (19²) and 400 (20²), so it is not a perfect square. It is not a perfect cube.
364 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 364.
Distinguish a square from a square rootMultiplication table for 364
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 | 182 | 0 | Yes |
| 3 | 121 | 1 | No |
| 4 | 91 | 0 | Yes |
| 5 | 72 | 4 | No |
| 6 | 60 | 4 | No |
| 7 | 52 | 0 | Yes |
| 8 | 45 | 4 | No |
| 9 | 40 | 4 | No |
| 10 | 36 | 4 | No |
| 11 | 33 | 1 | No |
| 12 | 30 | 4 | No |
For example, 364 = 7 × 52 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 364
364 contains 3 decimal digits. Its digit sum is 3 + 6 + 4 = 13.
- 364: 3 + 6 + 4 = 13
- 13: 1 + 3 = 4
The digital root is 4. Reversing its digits gives 463; 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, 364/100 simplifies to 91/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 3.64. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 364 and 12 is 4. Their least common multiple is 1092. The identity GCD × LCM = 364 × 12 = 4368 checks both results.
Work through GCF and LCMQuestions about 364
What are the factors of 364?
The positive factors are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364. There are 12 factors, including 1 and 364.
Is 364 a prime number?
No. 364 is composite: 2^2 × 7 × 13 = 364.
How do you write 364 in Roman numerals?
364 is CCCLXIV in standard subtractive Roman numeral notation.
What is the binary representation of 364?
364 in decimal is 101101100 in base 2. Adding its active place values gives 256 + 64 + 32 + 8 + 4 = 364.
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 364
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 364 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.