Number dictionary · Exact arithmetic
384: factors and number facts
three hundred eighty-four is an even number and is composite. Its 16 positive divisors form 8 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- three hundred eighty-four
- Roman numeral
- CCCLXXXIV
- Prime factorization
- 2^7 × 3
- Digital root
- 6
All factors of 384
A positive factor divides 384 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
Factor pairs
- 1 × 384 = 384
- 2 × 192 = 384
- 3 × 128 = 384
- 4 × 96 = 384
- 6 × 64 = 384
- 8 × 48 = 384
- 12 × 32 = 384
- 16 × 24 = 384
Each pair describes an arrangement of 384 items into equal rows. The pairs have different row and column counts; 384 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 16
- Sum of all divisors
- 1020
- Sum excluding 384
- 636
- Classification
- abundant
384 is abundant because its proper divisors add to 636, which is greater than 384.
Prime factorization of 384
384 = 2^7 × 3
Repeated division, step by step
- 384 ÷ 2 = 192
- 192 ÷ 2 = 96
- 96 ÷ 2 = 48
- 48 ÷ 2 = 24
- 24 ÷ 2 = 12
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3
- 3 ÷ 3 = 1
Multiply the prime divisors in these steps to reconstruct 384. An exponent records how many times the same prime occurs. The divisor-count calculation is (7 + 1) × (1 + 1) = 16.
The preceding prime is 383. The next larger prime is 389. The factor list above explains why 384 is composite.
Learn the factorization method384 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred eighty-four |
| Roman numeral | CCCLXXXIV |
| Binary (base 2) | 110000000 |
| Octal (base 8) | 600 |
| Decimal (base 10) | 384 |
| Hexadecimal (base 16) | 180 |
Check the binary conversion
Read 110000000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
256 + 128 = 384
Check the hexadecimal conversion
1 × 16^2 + 8 × 16^1 + 0 × 16^0 = 384
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 384
- 384 squared
- 384 × 384 = 147,456
- 384 cubed
- 384 × 384 × 384 = 56,623,104
- Square root
- ≈ 19.595918
- Simplified radical
- 8√6
384 lies between 361 (19²) and 400 (20²), so it is not a perfect square. It is not a perfect cube.
384 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 384.
Distinguish a square from a square rootMultiplication table for 384
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 | 192 | 0 | Yes |
| 3 | 128 | 0 | Yes |
| 4 | 96 | 0 | Yes |
| 5 | 76 | 4 | No |
| 6 | 64 | 0 | Yes |
| 7 | 54 | 6 | No |
| 8 | 48 | 0 | Yes |
| 9 | 42 | 6 | No |
| 10 | 38 | 4 | No |
| 11 | 34 | 10 | No |
| 12 | 32 | 0 | Yes |
For example, 384 = 7 × 54 + 6. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 384
384 contains 3 decimal digits. Its digit sum is 3 + 8 + 4 = 15.
- 384: 3 + 8 + 4 = 15
- 15: 1 + 5 = 6
The digital root is 6. Reversing its digits gives 483; 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, 384/100 simplifies to 96/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 3.84. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 384 and 12 is 12. Their least common multiple is 384. The identity GCD × LCM = 384 × 12 = 4608 checks both results.
Work through GCF and LCMQuestions about 384
What are the factors of 384?
The positive factors are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384. There are 16 factors, including 1 and 384.
Is 384 a prime number?
No. 384 is composite: 2^7 × 3 = 384.
How do you write 384 in Roman numerals?
384 is CCCLXXXIV in standard subtractive Roman numeral notation.
What is the binary representation of 384?
384 in decimal is 110000000 in base 2. Adding its active place values gives 256 + 128 = 384.
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 384
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 384 add to 15. 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.