The number 31984
31984 is a composite number with 10 divisors. Its prime factorisation is × 1999. Divisors (10): 1, 2, 4, 8, 16, 1999, 3998, 7996, 15992, 31984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
31984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
31984 is composite. Its prime factorisation is
- 3
The divisors add up to 62000; without 31984 itself that is 30016, so 31984 is deficient (30016 is less than 31984). Euler's totient φ(31984) = 15984 numbers up to 31984 share no factor with it.
- 4
The digits of 31984 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31984 = 2^{4} \times 1999 \]31984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 10 |
| Sum of divisors | 62000 |
| Euler totient φ(n) | 15984 |
| Square | 1022976256 |
| Cube | 32718872571904 |
| Square root | 178.840711 (= 4√1999) |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.1984 × |
31984 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand nine hundred and eighty-four |
| Binary (base 2) | 111110011110000 |
| Octal (base 8) | 76360 |
| Hexadecimal (base 16) | 7CF0 |
| Base 3 | 1121212121 |
| As time | 31984 seconds = 8 h 53 min 4 s |
Is 31984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31984 ÷ 2 = 15992) | 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 (31984 ÷ 4 = 7996) | 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 1) | 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 (31984 ÷ 8 = 3998) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 7) | 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 31984 a prime number?
No. 31984 = × 1999, so it is divisible by 2.
What are the factors of 31984?
1, 2, 4, 8, 16, 1999, 3998, 7996, 15992, 31984.
What is 31984 in binary?
111110011110000 (hexadecimal 7CF0, octal 76360).
What is the square root of 31984?
About 178.8407, exactly 4√1999.
Is 31984 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 31984?
It is a composite number with 10 divisors.