The number 5840
5840 is a composite number with 20 divisors. Its prime factorisation is × 5 × 73. Divisors (20): 1, 2, 4, 5, 8, 10, 16, 20, 40, 73, 80, 146, 292, 365, 584, 730 … 5840.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
5840 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
5840 is composite. Its prime factorisation is
- 3
The divisors add up to 13764; without 5840 itself that is 7924, so 5840 is abundant (7924 is more than 5840). Euler's totient φ(5840) = 2304 numbers up to 5840 share no factor with it.
- 4
The digits of 5840 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 98 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5840 = 2^{4} \times 5 \times 73 \]5840 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 13764 |
| Euler totient φ(n) | 2304 |
| Square | 34105600 |
| Cube | 199176704000 |
| Square root | 76.419893 (= 4√365) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 98 |
| Scientific notation | 5.84 × |
5840 in other forms
| Form | Value |
|---|---|
| In words | five thousand eight hundred and forty |
| Binary (base 2) | 1011011010000 |
| Octal (base 8) | 13320 |
| Hexadecimal (base 16) | 16D0 |
| Base 3 | 22000022 |
| As time | 5840 seconds = 1 h 37 min 20 s |
Is 5840 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5840 ÷ 2 = 2920) | 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 (5840 ÷ 4 = 1460) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (5840 ÷ 5 = 1168) | 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 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 | Yes (5840 ÷ 8 = 730) | 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 | Yes (5840 ÷ 10 = 584) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 5840 a prime number?
No. 5840 = × 5 × 73, so it is divisible by 2.
What are the factors of 5840?
1, 2, 4, 5, 8, 10, 16, 20, 40, 73, 80, 146, 292, 365, 584, 730, 1168, 1460, 2920, 5840.
What is 5840 in binary?
1011011010000 (hexadecimal 16D0, octal 13320).
What is the square root of 5840?
About 76.4199, exactly 4√365.
Is 5840 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 5840?
It is a composite number with 20 divisors.