Number dictionary · Exact arithmetic
378: factors and number facts
three hundred seventy-eight 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 seventy-eight
- Roman numeral
- CCCLXXVIII
- Prime factorization
- 2 × 3^3 × 7
- Digital root
- 9
All factors of 378
A positive factor divides 378 with no remainder. In ascending order, the complete list is:
1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
Factor pairs
- 1 × 378 = 378
- 2 × 189 = 378
- 3 × 126 = 378
- 6 × 63 = 378
- 7 × 54 = 378
- 9 × 42 = 378
- 14 × 27 = 378
- 18 × 21 = 378
Each pair describes an arrangement of 378 items into equal rows. The pairs have different row and column counts; 378 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 16
- Sum of all divisors
- 960
- Sum excluding 378
- 582
- Classification
- abundant
378 is abundant because its proper divisors add to 582, which is greater than 378.
Prime factorization of 378
378 = 2 × 3^3 × 7
Repeated division, step by step
- 378 ÷ 2 = 189
- 189 ÷ 3 = 63
- 63 ÷ 3 = 21
- 21 ÷ 3 = 7
- 7 ÷ 7 = 1
Multiply the prime divisors in these steps to reconstruct 378. An exponent records how many times the same prime occurs. The divisor-count calculation is (1 + 1) × (3 + 1) × (1 + 1) = 16.
The preceding prime is 373. The next larger prime is 379. The factor list above explains why 378 is composite.
Learn the factorization method378 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred seventy-eight |
| Roman numeral | CCCLXXVIII |
| Binary (base 2) | 101111010 |
| Octal (base 8) | 572 |
| Decimal (base 10) | 378 |
| Hexadecimal (base 16) | 17A |
Check the binary conversion
Read 101111010 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 + 2 = 378
Check the hexadecimal conversion
1 × 16^2 + 7 × 16^1 + 10 × 16^0 = 378
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 378
- 378 squared
- 378 × 378 = 142,884
- 378 cubed
- 378 × 378 × 378 = 54,010,152
- Square root
- ≈ 19.442222
- Simplified radical
- 3√42
378 lies between 361 (19²) and 400 (20²), so it is not a perfect square. It is not a perfect cube.
378 is triangular: it is the sum of the integers from 1 through 27.
Distinguish a square from a square rootMultiplication table for 378
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 | 189 | 0 | Yes |
| 3 | 126 | 0 | Yes |
| 4 | 94 | 2 | No |
| 5 | 75 | 3 | No |
| 6 | 63 | 0 | Yes |
| 7 | 54 | 0 | Yes |
| 8 | 47 | 2 | No |
| 9 | 42 | 0 | Yes |
| 10 | 37 | 8 | No |
| 11 | 34 | 4 | No |
| 12 | 31 | 6 | No |
For example, 378 = 7 × 54 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 378
378 contains 3 decimal digits. Its digit sum is 3 + 7 + 8 = 18.
- 378: 3 + 7 + 8 = 18
- 18: 1 + 8 = 9
The digital root is 9. Reversing its digits gives 873; 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, 378/100 simplifies to 189/50 by dividing both terms by their greatest common divisor, 2. Its decimal value is 3.78. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 378 and 12 is 6. Their least common multiple is 756. The identity GCD × LCM = 378 × 12 = 4536 checks both results.
Work through GCF and LCMQuestions about 378
What are the factors of 378?
The positive factors are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378. There are 16 factors, including 1 and 378.
Is 378 a prime number?
No. 378 is composite: 2 × 3^3 × 7 = 378.
How do you write 378 in Roman numerals?
378 is CCCLXXVIII in standard subtractive Roman numeral notation.
What is the binary representation of 378?
378 in decimal is 101111010 in base 2. Adding its active place values gives 256 + 64 + 32 + 16 + 8 + 2 = 378.
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 378
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 378 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.