The number 392
392 is a composite number with 12 divisors. Its prime factorisation is × . Divisors (12): 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 392: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 14.
- 2
392 is composite. Its prime factorisation is
- 3
The divisors add up to 855; without 392 itself that is 463, so 392 is abundant (463 is more than 392). Euler's totient φ(392) = 168 numbers up to 392 share no factor with it.
- 4
The digits of 392 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 27 steps to reach 1.
LaTeX source of the formulas on this page
\[ 392 = 2^{3} \times 7^{2} \]392 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 855 |
| Euler totient φ(n) | 168 |
| Square | 153664 |
| Cube | 60236288 |
| Square root | 19.798990 (= 14√2) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 27 |
| Scientific notation | 3.92 × |
392 in other forms
| Form | Value |
|---|---|
| In words | three hundred and ninety-two |
| Roman numerals | CCCXCII |
| Binary (base 2) | 110001000 |
| Octal (base 8) | 610 |
| Hexadecimal (base 16) | 188 |
| Base 3 | 112112 |
| As time | 392 seconds = 6 min 32 s |
Is 392 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (392 ÷ 2 = 196) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (392 ÷ 4 = 98) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (392 ÷ 7 = 56) | 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 | Yes (392 ÷ 8 = 49) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 392 a prime number?
No. 392 = × , so it is divisible by 2.
What are the factors of 392?
1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392.
What is 392 in binary?
110001000 (hexadecimal 188, octal 610).
What is the square root of 392?
About 19.7990, exactly 14√2.
What is 392 in Roman numerals?
CCCXCII.
Is 392 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 392?
392 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 14.