The number 61584
61584 is a composite number with 20 divisors. Its prime factorisation is × 3 × 1283. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1283, 2566, 3849, 5132, 7698, 10264 … 61584.
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How to work it out
- 1
What is special about 61584: a Harshad number: divisible by its digit sum 24.
- 2
61584 is composite. Its prime factorisation is
- 3
The divisors add up to 159216; without 61584 itself that is 97632, so 61584 is abundant (97632 is more than 61584). Euler's totient φ(61584) = 20512 numbers up to 61584 share no factor with it.
- 4
The digits of 61584 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 61584 = 2^{4} \times 3 \times 1283 \]61584 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 159216 |
| Euler totient φ(n) | 20512 |
| Square | 3792589056 |
| Cube | 233562804424704 |
| Square root | 248.161238 (= 4√3849) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 135 |
| Scientific notation | 6.1584 × |
61584 in other forms
| Form | Value |
|---|---|
| In words | sixty-one thousand five hundred and eighty-four |
| Binary (base 2) | 1111000010010000 |
| Octal (base 8) | 170220 |
| Hexadecimal (base 16) | F090 |
| Base 3 | 10010110220 |
| As time | 61584 seconds = 17 h 6 min 24 s |
Is 61584 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (61584 ÷ 2 = 30792) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (61584 ÷ 3 = 20528) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (61584 ÷ 4 = 15396) | 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 (61584 ÷ 6 = 10264) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (61584 ÷ 8 = 7698) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (61584 ÷ 12 = 5132) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 61584 a prime number?
No. 61584 = × 3 × 1283, so it is divisible by 2.
What are the factors of 61584?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1283, 2566, 3849, 5132, 7698, 10264, 15396, 20528, 30792, 61584.
What is 61584 in binary?
1111000010010000 (hexadecimal F090, octal 170220).
What is the square root of 61584?
About 248.1612, exactly 4√3849.
Is 61584 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 61584?
61584 is a Harshad number: divisible by its digit sum 24.