The number 3584
3584 is a composite number with 20 divisors. Its prime factorisation is × 7. Divisors (20): 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448 … 3584.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
3584 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
3584 is composite. Its prime factorisation is
- 3
The divisors add up to 8184; without 3584 itself that is 4600, so 3584 is abundant (4600 is more than 3584). Euler's totient φ(3584) = 1536 numbers up to 3584 share no factor with it.
- 4
The digits of 3584 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 25 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3584 = 2^{9} \times 7 \]3584 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 8184 |
| Euler totient φ(n) | 1536 |
| Square | 12845056 |
| Cube | 46036680704 |
| Square root | 59.866518 (= 16√14) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 25 |
| Scientific notation | 3.584 × |
3584 in other forms
| Form | Value |
|---|---|
| In words | three thousand five hundred and eighty-four |
| Roman numerals | MMMDLXXXIV |
| Binary (base 2) | 111000000000 |
| Octal (base 8) | 7000 |
| Hexadecimal (base 16) | E00 |
| Base 3 | 11220202 |
| As time | 3584 seconds = 59 min 44 s |
Is 3584 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3584 ÷ 2 = 1792) | 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 (3584 ÷ 4 = 896) | 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 | Yes (3584 ÷ 7 = 512) | 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 (3584 ÷ 8 = 448) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 9) | 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 3584 a prime number?
No. 3584 = × 7, so it is divisible by 2.
What are the factors of 3584?
1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792, 3584.
What is 3584 in binary?
111000000000 (hexadecimal E00, octal 7000).
What is the square root of 3584?
About 59.8665, exactly 16√14.
What is 3584 in Roman numerals?
MMMDLXXXIV.
Is 3584 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 3584?
It is a composite number with 20 divisors.