The number 1983
1983 is a composite number with 4 divisors. Its prime factorisation is 3 × 661. Divisors (4): 1, 3, 661, 1983.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1983: a semiprime: 3 × 661, the product of two primes.
- 2
1983 is composite. Its prime factorisation is
- 3
The divisors add up to 2648; without 1983 itself that is 665, so 1983 is deficient (665 is less than 1983). Euler's totient φ(1983) = 1320 numbers up to 1983 share no factor with it.
- 4
The digits of 1983 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1983 = 3 \times 661 \]
1983 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 2648 |
| Euler totient φ(n) | 1320 |
| Square | 3932289 |
| Cube | 7797729087 |
| Square root | 44.530888 |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 50 |
| Scientific notation | 1.983 × |
1983 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and eighty-three |
| Roman numerals | MCMLXXXIII |
| Binary (base 2) | 11110111111 |
| Octal (base 8) | 3677 |
| Hexadecimal (base 16) | 7BF |
| Base 3 | 2201110 |
| As time | 1983 seconds = 33 min 3 s |
Is 1983 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 (1983 ÷ 3 = 661) | 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 2) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 | No (remainder 3) | 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 1983 a prime number?
No. 1983 = 3 × 661, so it is divisible by 3.
What are the factors of 1983?
1, 3, 661, 1983.
What is 1983 in binary?
11110111111 (hexadecimal 7BF, octal 3677).
What is the square root of 1983?
About 44.5309.
What is 1983 in Roman numerals?
MCMLXXXIII.
Is 1983 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 1983?
1983 is a semiprime: 3 × 661, the product of two primes.