The number 1584
1584 is a composite number with 30 divisors. Its prime factorisation is × × 11. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 33, 36, 44 … 1584.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1584: a Harshad number: divisible by its digit sum 18.
- 2
1584 is composite. Its prime factorisation is
- 3
The divisors add up to 4836; without 1584 itself that is 3252, so 1584 is abundant (3252 is more than 1584). Euler's totient φ(1584) = 480 numbers up to 1584 share no factor with it.
- 4
The digits of 1584 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1584 = 2^{4} \times 3^{2} \times 11 \]1584 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 4836 |
| Euler totient φ(n) | 480 |
| Square | 2509056 |
| Cube | 3974344704 |
| Square root | 39.799497 (= 12√11) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 29 |
| Scientific notation | 1.584 × |
1584 in other forms
| Form | Value |
|---|---|
| In words | one thousand five hundred and eighty-four |
| Roman numerals | MDLXXXIV |
| Binary (base 2) | 11000110000 |
| Octal (base 8) | 3060 |
| Hexadecimal (base 16) | 630 |
| Base 3 | 2011200 |
| As time | 1584 seconds = 26 min 24 s |
Is 1584 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1584 ÷ 2 = 792) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1584 ÷ 3 = 528) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1584 ÷ 4 = 396) | 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 | Yes (1584 ÷ 6 = 264) | 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 (1584 ÷ 8 = 198) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1584 ÷ 9 = 176) | 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 (1584 ÷ 11 = 144) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1584 ÷ 12 = 132) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1584 a prime number?
No. 1584 = × × 11, so it is divisible by 2.
What are the factors of 1584?
1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 33, 36, 44, 48, 66, 72, 88, 99, 132, 144, 176, 198, 264, 396, 528, 792, 1584.
What is 1584 in binary?
11000110000 (hexadecimal 630, octal 3060).
What is the square root of 1584?
About 39.7995, exactly 12√11.
What is 1584 in Roman numerals?
MDLXXXIV.
Is 1584 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1584?
1584 is a Harshad number: divisible by its digit sum 18.