Number dictionary · Exact arithmetic
380: factors and number facts
three hundred eighty 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 eighty
- Roman numeral
- CCCLXXX
- Prime factorization
- 2^2 × 5 × 19
- Digital root
- 2
All factors of 380
A positive factor divides 380 with no remainder. In ascending order, the complete list is:
1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380
Factor pairs
- 1 × 380 = 380
- 2 × 190 = 380
- 4 × 95 = 380
- 5 × 76 = 380
- 10 × 38 = 380
- 19 × 20 = 380
Each pair describes an arrangement of 380 items into equal rows. The pairs have different row and column counts; 380 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 12
- Sum of all divisors
- 840
- Sum excluding 380
- 460
- Classification
- abundant
380 is abundant because its proper divisors add to 460, which is greater than 380.
Prime factorization of 380
380 = 2^2 × 5 × 19
Repeated division, step by step
- 380 ÷ 2 = 190
- 190 ÷ 2 = 95
- 95 ÷ 5 = 19
- 19 ÷ 19 = 1
Multiply the prime divisors in these steps to reconstruct 380. 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 379. The next larger prime is 383. The factor list above explains why 380 is composite.
Learn the factorization method380 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred eighty |
| Roman numeral | CCCLXXX |
| Binary (base 2) | 101111100 |
| Octal (base 8) | 574 |
| Decimal (base 10) | 380 |
| Hexadecimal (base 16) | 17C |
Check the binary conversion
Read 101111100 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 + 16 + 8 + 4 = 380
Check the hexadecimal conversion
1 × 16^2 + 7 × 16^1 + 12 × 16^0 = 380
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 380
- 380 squared
- 380 × 380 = 144,400
- 380 cubed
- 380 × 380 × 380 = 54,872,000
- Square root
- ≈ 19.493589
- Simplified radical
- 2√95
380 lies between 361 (19²) and 400 (20²), so it is not a perfect square. It is not a perfect cube.
380 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 380.
Distinguish a square from a square rootMultiplication table for 380
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 | 190 | 0 | Yes |
| 3 | 126 | 2 | No |
| 4 | 95 | 0 | Yes |
| 5 | 76 | 0 | Yes |
| 6 | 63 | 2 | No |
| 7 | 54 | 2 | No |
| 8 | 47 | 4 | No |
| 9 | 42 | 2 | No |
| 10 | 38 | 0 | Yes |
| 11 | 34 | 6 | No |
| 12 | 31 | 8 | No |
For example, 380 = 7 × 54 + 2. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 380
380 contains 3 decimal digits. Its digit sum is 3 + 8 + 0 = 11.
- 380: 3 + 8 + 0 = 11
- 11: 1 + 1 = 2
The digital root is 2. Reversing its digits gives 083; 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, 380/100 simplifies to 19/5 by dividing both terms by their greatest common divisor, 20. Its decimal value is 3.8. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 380 and 12 is 4. Their least common multiple is 1140. The identity GCD × LCM = 380 × 12 = 4560 checks both results.
Work through GCF and LCMQuestions about 380
What are the factors of 380?
The positive factors are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380. There are 12 factors, including 1 and 380.
Is 380 a prime number?
No. 380 is composite: 2^2 × 5 × 19 = 380.
How do you write 380 in Roman numerals?
380 is CCCLXXX in standard subtractive Roman numeral notation.
What is the binary representation of 380?
380 in decimal is 101111100 in base 2. Adding its active place values gives 256 + 64 + 32 + 16 + 8 + 4 = 380.
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 380
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 380 add to 11. 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.