Number dictionary · Exact arithmetic
387: factors and number facts
three hundred eighty-seven is an odd number and is composite. Its 6 positive divisors form 3 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- three hundred eighty-seven
- Roman numeral
- CCCLXXXVII
- Prime factorization
- 3^2 × 43
- Digital root
- 9
All factors of 387
A positive factor divides 387 with no remainder. In ascending order, the complete list is:
1, 3, 9, 43, 129, 387
Factor pairs
- 1 × 387 = 387
- 3 × 129 = 387
- 9 × 43 = 387
Each pair describes an arrangement of 387 items into equal rows. The pairs have different row and column counts; 387 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 6
- Sum of all divisors
- 572
- Sum excluding 387
- 185
- Classification
- deficient
387 is deficient because its proper divisors add to 185, which is less than 387.
Prime factorization of 387
387 = 3^2 × 43
Repeated division, step by step
- 387 ÷ 3 = 129
- 129 ÷ 3 = 43
- 43 ÷ 43 = 1
Multiply the prime divisors in these steps to reconstruct 387. An exponent records how many times the same prime occurs. The divisor-count calculation is (2 + 1) × (1 + 1) = 6.
The preceding prime is 383. The next larger prime is 389. The factor list above explains why 387 is composite.
Learn the factorization method387 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred eighty-seven |
| Roman numeral | CCCLXXXVII |
| Binary (base 2) | 110000011 |
| Octal (base 8) | 603 |
| Decimal (base 10) | 387 |
| Hexadecimal (base 16) | 183 |
Check the binary conversion
Read 110000011 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 + 2 + 1 = 387
Check the hexadecimal conversion
1 × 16^2 + 8 × 16^1 + 3 × 16^0 = 387
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 387
- 387 squared
- 387 × 387 = 149,769
- 387 cubed
- 387 × 387 × 387 = 57,960,603
- Square root
- ≈ 19.672316
- Simplified radical
- 3√43
387 lies between 361 (19²) and 400 (20²), so it is not a perfect square. It is not a perfect cube.
387 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 387.
Distinguish a square from a square rootMultiplication table for 387
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 | 193 | 1 | No |
| 3 | 129 | 0 | Yes |
| 4 | 96 | 3 | No |
| 5 | 77 | 2 | No |
| 6 | 64 | 3 | No |
| 7 | 55 | 2 | No |
| 8 | 48 | 3 | No |
| 9 | 43 | 0 | Yes |
| 10 | 38 | 7 | No |
| 11 | 35 | 2 | No |
| 12 | 32 | 3 | No |
For example, 387 = 7 × 55 + 2. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 387
387 contains 3 decimal digits. Its digit sum is 3 + 8 + 7 = 18.
- 387: 3 + 8 + 7 = 18
- 18: 1 + 8 = 9
The digital root is 9. Reversing its digits gives 783; 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, 387/100 simplifies to 387/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 3.87. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 387 and 12 is 3. Their least common multiple is 1548. The identity GCD × LCM = 387 × 12 = 4644 checks both results.
Work through GCF and LCMQuestions about 387
What are the factors of 387?
The positive factors are 1, 3, 9, 43, 129, 387. There are 6 factors, including 1 and 387.
Is 387 a prime number?
No. 387 is composite: 3^2 × 43 = 387.
How do you write 387 in Roman numerals?
387 is CCCLXXXVII in standard subtractive Roman numeral notation.
What is the binary representation of 387?
387 in decimal is 110000011 in base 2. Adding its active place values gives 256 + 128 + 2 + 1 = 387.
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 387
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 387 add to 18. 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.