The number 5984
5984 is a composite number with 24 divisors. Its prime factorisation is × 11 × 17. Divisors (24): 1, 2, 4, 8, 11, 16, 17, 22, 32, 34, 44, 68, 88, 136, 176, 187 … 5984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
5984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
5984 is composite. Its prime factorisation is
- 3
The divisors add up to 13608; without 5984 itself that is 7624, so 5984 is abundant (7624 is more than 5984). Euler's totient φ(5984) = 2560 numbers up to 5984 share no factor with it.
- 4
The digits of 5984 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5984 = 2^{5} \times 11 \times 17 \]5984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 13608 |
| Euler totient φ(n) | 2560 |
| Square | 35808256 |
| Cube | 214276603904 |
| Square root | 77.356318 (= 4√374) |
| Digit sum / digital root | 26 / 8 |
| Collatz steps to 1 | 49 |
| Scientific notation | 5.984 × |
5984 in other forms
| Form | Value |
|---|---|
| In words | five thousand nine hundred and eighty-four |
| Binary (base 2) | 1011101100000 |
| Octal (base 8) | 13540 |
| Hexadecimal (base 16) | 1760 |
| Base 3 | 22012122 |
| As time | 5984 seconds = 1 h 39 min 44 s |
Is 5984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5984 ÷ 2 = 2992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (5984 ÷ 4 = 1496) | 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 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (5984 ÷ 8 = 748) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 | Yes (5984 ÷ 11 = 544) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5984 a prime number?
No. 5984 = × 11 × 17, so it is divisible by 2.
What are the factors of 5984?
1, 2, 4, 8, 11, 16, 17, 22, 32, 34, 44, 68, 88, 136, 176, 187, 272, 352, 374, 544, 748, 1496, 2992, 5984.
What is 5984 in binary?
1011101100000 (hexadecimal 1760, octal 13540).
What is the square root of 5984?
About 77.3563, exactly 4√374.
Is 5984 divisible by 3?
No. Its digits add up to 26, which is not a multiple of 3.
What is special about the number 5984?
It is a composite number with 24 divisors.