The number 378
378 is a triangular number: 1 + 2 + … + 27 = 378. Its prime factorisation is 2 × × 7. Divisors (16): 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 378: a triangular number: 1 + 2 + … + 27 = 378; a Harshad number: divisible by its digit sum 18.
- 2
378 is composite. Its prime factorisation is
- 3
The divisors add up to 960; without 378 itself that is 582, so 378 is abundant (582 is more than 378). Euler's totient φ(378) = 108 numbers up to 378 share no factor with it.
- 4
The digits of 378 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 378 = 2 \times 3^{3} \times 7 \]378 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 960 |
| Euler totient φ(n) | 108 |
| Square | 142884 |
| Cube | 54010152 |
| Square root | 19.442222 (= 3√42) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 107 |
| Scientific notation | 3.78 × |
378 in other forms
| Form | Value |
|---|---|
| In words | three hundred and seventy-eight |
| Roman numerals | CCCLXXVIII |
| Binary (base 2) | 101111010 |
| Octal (base 8) | 572 |
| Hexadecimal (base 16) | 17A |
| Base 3 | 112000 |
| As time | 378 seconds = 6 min 18 s |
Is 378 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (378 ÷ 2 = 189) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (378 ÷ 3 = 126) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (378 ÷ 6 = 63) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (378 ÷ 7 = 54) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | No (remainder 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (378 ÷ 9 = 42) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 378 a prime number?
No. 378 = 2 × × 7, so it is divisible by 2.
What are the factors of 378?
1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378.
What is 378 in binary?
101111010 (hexadecimal 17A, octal 572).
What is the square root of 378?
About 19.4422, exactly 3√42.
What is 378 in Roman numerals?
CCCLXXVIII.
Is 378 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 378?
378 is a triangular number: 1 + 2 + … + 27 = 378; a Harshad number: divisible by its digit sum 18.