The number 67824
67824 is a composite number with 40 divisors. Its prime factorisation is × × 157. Divisors (40): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72 … 67824.
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How to work it out
- 1
What is special about 67824: a Harshad number: divisible by its digit sum 27.
- 2
67824 is composite. Its prime factorisation is
- 3
The divisors add up to 195920; without 67824 itself that is 128096, so 67824 is abundant (128096 is more than 67824). Euler's totient φ(67824) = 22464 numbers up to 67824 share no factor with it.
- 4
The digits of 67824 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 86 steps to reach 1.
LaTeX source of the formulas on this page
\[ 67824 = 2^{4} \times 3^{3} \times 157 \]67824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 195920 |
| Euler totient φ(n) | 22464 |
| Square | 4600094976 |
| Cube | 311996841652224 |
| Square root | 260.430413 (= 12√471) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 86 |
| Scientific notation | 6.7824 × |
67824 in other forms
| Form | Value |
|---|---|
| In words | sixty-seven thousand eight hundred and twenty-four |
| Binary (base 2) | 10000100011110000 |
| Octal (base 8) | 204360 |
| Hexadecimal (base 16) | 108F0 |
| Base 3 | 10110001000 |
| As time | 67824 seconds = 18 h 50 min 24 s |
Is 67824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (67824 ÷ 2 = 33912) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (67824 ÷ 3 = 22608) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (67824 ÷ 4 = 16956) | 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 (67824 ÷ 6 = 11304) | 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 (67824 ÷ 8 = 8478) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (67824 ÷ 9 = 7536) | 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 | Yes (67824 ÷ 12 = 5652) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 67824 a prime number?
No. 67824 = × × 157, so it is divisible by 2.
What are the factors of 67824?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 157, 216, 314, 432, 471, 628, 942, 1256, 1413, 1884, 2512, 2826, 3768, 4239, 5652, 7536, 8478, 11304, 16956, 22608, 33912, 67824.
What is 67824 in binary?
10000100011110000 (hexadecimal 108F0, octal 204360).
What is the square root of 67824?
About 260.4304, exactly 12√471.
Is 67824 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 67824?
67824 is a Harshad number: divisible by its digit sum 27.