Number dictionary · Exact arithmetic
390: factors and number facts
three hundred ninety 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 ninety
- Roman numeral
- CCCXC
- Prime factorization
- 2 × 3 × 5 × 13
- Digital root
- 3
All factors of 390
A positive factor divides 390 with no remainder. In ascending order, the complete list is:
1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
Factor pairs
- 1 × 390 = 390
- 2 × 195 = 390
- 3 × 130 = 390
- 5 × 78 = 390
- 6 × 65 = 390
- 10 × 39 = 390
- 13 × 30 = 390
- 15 × 26 = 390
Each pair describes an arrangement of 390 items into equal rows. The pairs have different row and column counts; 390 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 16
- Sum of all divisors
- 1008
- Sum excluding 390
- 618
- Classification
- abundant
390 is abundant because its proper divisors add to 618, which is greater than 390.
Prime factorization of 390
390 = 2 × 3 × 5 × 13
Repeated division, step by step
- 390 ÷ 2 = 195
- 195 ÷ 3 = 65
- 65 ÷ 5 = 13
- 13 ÷ 13 = 1
Multiply the prime divisors in these steps to reconstruct 390. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 16.
The preceding prime is 389. The next larger prime is 397. The factor list above explains why 390 is composite.
Learn the factorization method390 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred ninety |
| Roman numeral | CCCXC |
| Binary (base 2) | 110000110 |
| Octal (base 8) | 606 |
| Decimal (base 10) | 390 |
| Hexadecimal (base 16) | 186 |
Check the binary conversion
Read 110000110 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 + 4 + 2 = 390
Check the hexadecimal conversion
1 × 16^2 + 8 × 16^1 + 6 × 16^0 = 390
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 390
- 390 squared
- 390 × 390 = 152,100
- 390 cubed
- 390 × 390 × 390 = 59,319,000
- Square root
- ≈ 19.748418
- Simplified radical
- √390
390 lies between 361 (19²) and 400 (20²), so it is not a perfect square. It is not a perfect cube.
390 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 390.
Distinguish a square from a square rootMultiplication table for 390
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 | 195 | 0 | Yes |
| 3 | 130 | 0 | Yes |
| 4 | 97 | 2 | No |
| 5 | 78 | 0 | Yes |
| 6 | 65 | 0 | Yes |
| 7 | 55 | 5 | No |
| 8 | 48 | 6 | No |
| 9 | 43 | 3 | No |
| 10 | 39 | 0 | Yes |
| 11 | 35 | 5 | No |
| 12 | 32 | 6 | No |
For example, 390 = 7 × 55 + 5. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 390
390 contains 3 decimal digits. Its digit sum is 3 + 9 + 0 = 12.
- 390: 3 + 9 + 0 = 12
- 12: 1 + 2 = 3
The digital root is 3. Reversing its digits gives 093; 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, 390/100 simplifies to 39/10 by dividing both terms by their greatest common divisor, 10. Its decimal value is 3.9. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 390 and 12 is 6. Their least common multiple is 780. The identity GCD × LCM = 390 × 12 = 4680 checks both results.
Work through GCF and LCMQuestions about 390
What are the factors of 390?
The positive factors are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390. There are 16 factors, including 1 and 390.
Is 390 a prime number?
No. 390 is composite: 2 × 3 × 5 × 13 = 390.
How do you write 390 in Roman numerals?
390 is CCCXC in standard subtractive Roman numeral notation.
What is the binary representation of 390?
390 in decimal is 110000110 in base 2. Adding its active place values gives 256 + 128 + 4 + 2 = 390.
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 390
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 390 add to 12. 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.