The number 1984
1984 is a composite number with 14 divisors. Its prime factorisation is × 31. Divisors (14): 1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, 992, 1984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1984 is composite. Its prime factorisation is
- 3
The divisors add up to 4064; without 1984 itself that is 2080, so 1984 is abundant (2080 is more than 1984). Euler's totient φ(1984) = 960 numbers up to 1984 share no factor with it.
- 4
The digits of 1984 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 112 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1984 = 2^{6} \times 31 \]1984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 14 |
| Sum of divisors | 4064 |
| Euler totient φ(n) | 960 |
| Square | 3936256 |
| Cube | 7809531904 |
| Square root | 44.542115 (= 8√31) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 112 |
| Scientific notation | 1.984 × |
1984 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and eighty-four |
| Roman numerals | MCMLXXXIV |
| Binary (base 2) | 11111000000 |
| Octal (base 8) | 3700 |
| Hexadecimal (base 16) | 7C0 |
| Base 3 | 2201111 |
| As time | 1984 seconds = 33 min 4 s |
Is 1984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1984 ÷ 2 = 992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1984 ÷ 4 = 496) | 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 | No (remainder 4) | 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 | Yes (1984 ÷ 8 = 248) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1984 a prime number?
No. 1984 = × 31, so it is divisible by 2.
What are the factors of 1984?
1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, 992, 1984.
What is 1984 in binary?
11111000000 (hexadecimal 7C0, octal 3700).
What is the square root of 1984?
About 44.5421, exactly 8√31.
What is 1984 in Roman numerals?
MCMLXXXIV.
Is 1984 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 1984?
It is a composite number with 14 divisors.