The number 1683
1683 is a composite number with 12 divisors. Its prime factorisation is × 11 × 17. Divisors (12): 1, 3, 9, 11, 17, 33, 51, 99, 153, 187, 561, 1683.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1683 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1683 is composite. Its prime factorisation is
- 3
The divisors add up to 2808; without 1683 itself that is 1125, so 1683 is deficient (1125 is less than 1683). Euler's totient φ(1683) = 960 numbers up to 1683 share no factor with it.
- 4
The digits of 1683 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 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1683 = 3^{2} \times 11 \times 17 \]1683 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 2808 |
| Euler totient φ(n) | 960 |
| Square | 2832489 |
| Cube | 4767078987 |
| Square root | 41.024383 (= 3√187) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.683 × |
1683 in other forms
| Form | Value |
|---|---|
| In words | one thousand six hundred and eighty-three |
| Roman numerals | MDCLXXXIII |
| Binary (base 2) | 11010010011 |
| Octal (base 8) | 3223 |
| Hexadecimal (base 16) | 693 |
| Base 3 | 2022100 |
| As time | 1683 seconds = 28 min 3 s |
Is 1683 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1683 ÷ 3 = 561) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | 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 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1683 ÷ 9 = 187) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (1683 ÷ 11 = 153) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1683 a prime number?
No. 1683 = × 11 × 17, so it is divisible by 3.
What are the factors of 1683?
1, 3, 9, 11, 17, 33, 51, 99, 153, 187, 561, 1683.
What is 1683 in binary?
11010010011 (hexadecimal 693, octal 3223).
What is the square root of 1683?
About 41.0244, exactly 3√187.
What is 1683 in Roman numerals?
MDCLXXXIII.
Is 1683 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1683?
It is a composite number with 12 divisors.