The number 684
684 is a composite number with 18 divisors. Its prime factorisation is × × 19. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228 … 684.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 684: a Harshad number: divisible by its digit sum 18.
- 2
684 is composite. Its prime factorisation is
- 3
The divisors add up to 1820; without 684 itself that is 1136, so 684 is abundant (1136 is more than 684). Euler's totient φ(684) = 216 numbers up to 684 share no factor with it.
- 4
The digits of 684 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 126 steps to reach 1.
LaTeX source of the formulas on this page
\[ 684 = 2^{2} \times 3^{2} \times 19 \]684 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 1820 |
| Euler totient φ(n) | 216 |
| Square | 467856 |
| Cube | 320013504 |
| Square root | 26.153394 (= 6√19) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 126 |
| Scientific notation | 6.84 × |
684 in other forms
| Form | Value |
|---|---|
| In words | six hundred and eighty-four |
| Roman numerals | DCLXXXIV |
| Binary (base 2) | 1010101100 |
| Octal (base 8) | 1254 |
| Hexadecimal (base 16) | 2AC |
| Base 3 | 221100 |
| As time | 684 seconds = 11 min 24 s |
Is 684 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (684 ÷ 2 = 342) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (684 ÷ 3 = 228) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (684 ÷ 4 = 171) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (684 ÷ 6 = 114) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (684 ÷ 9 = 76) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (684 ÷ 12 = 57) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 684 a prime number?
No. 684 = × × 19, so it is divisible by 2.
What are the factors of 684?
1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684.
What is 684 in binary?
1010101100 (hexadecimal 2AC, octal 1254).
What is the square root of 684?
About 26.1534, exactly 6√19.
What is 684 in Roman numerals?
DCLXXXIV.
Is 684 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 684?
684 is a Harshad number: divisible by its digit sum 18.