The number 72384
72384 is a composite number with 56 divisors. Its prime factorisation is × 3 × 13 × 29. Divisors (56): 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 29, 32, 39, 48, 52 … 72384.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72384: a Harshad number: divisible by its digit sum 24.
- 2
72384 is composite. Its prime factorisation is
- 3
The divisors add up to 213360; without 72384 itself that is 140976, so 72384 is abundant (140976 is more than 72384). Euler's totient φ(72384) = 21504 numbers up to 72384 share no factor with it.
- 4
The digits of 72384 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 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72384 = 2^{6} \times 3 \times 13 \times 29 \]72384 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 213360 |
| Euler totient φ(n) | 21504 |
| Square | 5239443456 |
| Cube | 379251875119104 |
| Square root | 269.042748 (= 8√1131) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 42 |
| Scientific notation | 7.2384 × |
72384 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand three hundred and eighty-four |
| Binary (base 2) | 10001101011000000 |
| Octal (base 8) | 215300 |
| Hexadecimal (base 16) | 11AC0 |
| Base 3 | 10200021220 |
| As time | 72384 seconds = 20 h 6 min 24 s |
Is 72384 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72384 ÷ 2 = 36192) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72384 ÷ 3 = 24128) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72384 ÷ 4 = 18096) | 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 (72384 ÷ 6 = 12064) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (72384 ÷ 8 = 9048) | 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 (72384 ÷ 12 = 6032) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72384 a prime number?
No. 72384 = × 3 × 13 × 29, so it is divisible by 2.
What are the factors of 72384?
1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 29, 32, 39, 48, 52, 58, 64, 78, 87, 96, 104, 116, 156, 174, 192, 208, 232, 312, 348, 377, 416, 464, 624, 696, 754, 832, 928, 1131, 1248, 1392, 1508, 1856, 2262, 2496, 2784, 3016, 4524, 5568, 6032, 9048, 12064, 18096, 24128, 36192, 72384.
What is 72384 in binary?
10001101011000000 (hexadecimal 11AC0, octal 215300).
What is the square root of 72384?
About 269.0427, exactly 8√1131.
Is 72384 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 72384?
72384 is a Harshad number: divisible by its digit sum 24.