The number 73728
73728 is a composite number with 42 divisors. Its prime factorisation is × . Divisors (42): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72 … 73728.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
73728 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
73728 is composite. Its prime factorisation is
- 3
The divisors add up to 212979; without 73728 itself that is 139251, so 73728 is abundant (139251 is more than 73728). Euler's totient φ(73728) = 24576 numbers up to 73728 share no factor with it.
- 4
The digits of 73728 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 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73728 = 2^{13} \times 3^{2} \]73728 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 212979 |
| Euler totient φ(n) | 24576 |
| Square | 5435817984 |
| Cube | 400771988324352 |
| Square root | 271.529004 (= 192√2) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 32 |
| Scientific notation | 7.3728 × |
73728 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand seven hundred and twenty-eight |
| Binary (base 2) | 10010000000000000 |
| Octal (base 8) | 220000 |
| Hexadecimal (base 16) | 12000 |
| Base 3 | 10202010200 |
| As time | 73728 seconds = 20 h 28 min 48 s |
Is 73728 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (73728 ÷ 2 = 36864) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (73728 ÷ 3 = 24576) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (73728 ÷ 4 = 18432) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (73728 ÷ 6 = 12288) | 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 (73728 ÷ 8 = 9216) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (73728 ÷ 9 = 8192) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 (73728 ÷ 12 = 6144) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 73728 a prime number?
No. 73728 = × , so it is divisible by 2.
What are the factors of 73728?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 512, 576, 768, 1024, 1152, 1536, 2048, 2304, 3072, 4096, 4608, 6144, 8192, 9216, 12288, 18432, 24576, 36864, 73728.
What is 73728 in binary?
10010000000000000 (hexadecimal 12000, octal 220000).
What is the square root of 73728?
About 271.5290, exactly 192√2.
Is 73728 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 73728?
It is a composite number with 42 divisors.