The number 73824
73824 is a composite number with 24 divisors. Its prime factorisation is × 3 × 769. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 769, 1538, 2307, 3076 … 73824.
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How to work it out
- 1
What is special about 73824: a Harshad number: divisible by its digit sum 24.
- 2
73824 is composite. Its prime factorisation is
- 3
The divisors add up to 194040; without 73824 itself that is 120216, so 73824 is abundant (120216 is more than 73824). Euler's totient φ(73824) = 24576 numbers up to 73824 share no factor with it.
- 4
The digits of 73824 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 156 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73824 = 2^{5} \times 3 \times 769 \]73824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 194040 |
| Euler totient φ(n) | 24576 |
| Square | 5449982976 |
| Cube | 402339543220224 |
| Square root | 271.705723 (= 4√4614) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 156 |
| Scientific notation | 7.3824 × |
73824 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand eight hundred and twenty-four |
| Binary (base 2) | 10010000001100000 |
| Octal (base 8) | 220140 |
| Hexadecimal (base 16) | 12060 |
| Base 3 | 10202021020 |
| As time | 73824 seconds = 20 h 30 min 24 s |
Is 73824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (73824 ÷ 2 = 36912) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (73824 ÷ 3 = 24608) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (73824 ÷ 4 = 18456) | 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 (73824 ÷ 6 = 12304) | 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 (73824 ÷ 8 = 9228) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (73824 ÷ 12 = 6152) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 73824 a prime number?
No. 73824 = × 3 × 769, so it is divisible by 2.
What are the factors of 73824?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 769, 1538, 2307, 3076, 4614, 6152, 9228, 12304, 18456, 24608, 36912, 73824.
What is 73824 in binary?
10010000001100000 (hexadecimal 12060, octal 220140).
What is the square root of 73824?
About 271.7057, exactly 4√4614.
Is 73824 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 73824?
73824 is a Harshad number: divisible by its digit sum 24.