The number 2584
2584 is a Fibonacci number. Its prime factorisation is × 17 × 19. Divisors (16): 1, 2, 4, 8, 17, 19, 34, 38, 68, 76, 136, 152, 323, 646, 1292, 2584.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2584: a Fibonacci number; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 19.
- 2
2584 is composite. Its prime factorisation is
- 3
The divisors add up to 5400; without 2584 itself that is 2816, so 2584 is abundant (2816 is more than 2584). Euler's totient φ(2584) = 1152 numbers up to 2584 share no factor with it.
- 4
The digits of 2584 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 102 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2584 = 2^{3} \times 17 \times 19 \]2584 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 5400 |
| Euler totient φ(n) | 1152 |
| Square | 6677056 |
| Cube | 17253512704 |
| Square root | 50.833060 (= 2√646) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 102 |
| Scientific notation | 2.584 × |
2584 in other forms
| Form | Value |
|---|---|
| In words | two thousand five hundred and eighty-four |
| Roman numerals | MMDLXXXIV |
| Binary (base 2) | 101000011000 |
| Octal (base 8) | 5030 |
| Hexadecimal (base 16) | A18 |
| Base 3 | 10112201 |
| As time | 2584 seconds = 43 min 4 s |
Is 2584 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2584 ÷ 2 = 1292) | 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 (2584 ÷ 4 = 646) | 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 (2584 ÷ 8 = 323) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 10) | 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 2584 a prime number?
No. 2584 = × 17 × 19, so it is divisible by 2.
What are the factors of 2584?
1, 2, 4, 8, 17, 19, 34, 38, 68, 76, 136, 152, 323, 646, 1292, 2584.
What is 2584 in binary?
101000011000 (hexadecimal A18, octal 5030).
What is the square root of 2584?
About 50.8331, exactly 2√646.
What is 2584 in Roman numerals?
MMDLXXXIV.
Is 2584 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 2584?
2584 is a Fibonacci number; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 19.