The number 24864
24864 is a composite number with 48 divisors. Its prime factorisation is × 3 × 7 × 37. Divisors (48): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 37, 42 … 24864.
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How to work it out
- 1
What is special about 24864: a Harshad number: divisible by its digit sum 24.
- 2
24864 is composite. Its prime factorisation is
- 3
The divisors add up to 76608; without 24864 itself that is 51744, so 24864 is abundant (51744 is more than 24864). Euler's totient φ(24864) = 6912 numbers up to 24864 share no factor with it.
- 4
The digits of 24864 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 38 steps to reach 1.
LaTeX source of the formulas on this page
\[ 24864 = 2^{5} \times 3 \times 7 \times 37 \]24864 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 76608 |
| Euler totient φ(n) | 6912 |
| Square | 618218496 |
| Cube | 15371384684544 |
| Square root | 157.683227 (= 4√1554) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 38 |
| Scientific notation | 2.4864 × |
24864 in other forms
| Form | Value |
|---|---|
| In words | twenty-four thousand eight hundred and sixty-four |
| Binary (base 2) | 110000100100000 |
| Octal (base 8) | 60440 |
| Hexadecimal (base 16) | 6120 |
| Base 3 | 1021002220 |
| As time | 24864 seconds = 6 h 54 min 24 s |
Is 24864 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (24864 ÷ 2 = 12432) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (24864 ÷ 3 = 8288) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (24864 ÷ 4 = 6216) | 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 (24864 ÷ 6 = 4144) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (24864 ÷ 7 = 3552) | 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 (24864 ÷ 8 = 3108) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (24864 ÷ 12 = 2072) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 24864 a prime number?
No. 24864 = × 3 × 7 × 37, so it is divisible by 2.
What are the factors of 24864?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 37, 42, 48, 56, 74, 84, 96, 111, 112, 148, 168, 222, 224, 259, 296, 336, 444, 518, 592, 672, 777, 888, 1036, 1184, 1554, 1776, 2072, 3108, 3552, 4144, 6216, 8288, 12432, 24864.
What is 24864 in binary?
110000100100000 (hexadecimal 6120, octal 60440).
What is the square root of 24864?
About 157.6832, exactly 4√1554.
Is 24864 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 24864?
24864 is a Harshad number: divisible by its digit sum 24.