The number 65728
65728 is a taxicab number: it is the sum of two cubes in 2 ways (12³ + 40³ and 31³ + 33³). Its prime factorisation is × 13 × 79. Divisors (28): 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 79, 104, 158, 208, 316, 416 … 65728.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 65728: a taxicab number: it is the sum of two cubes in 2 ways (12³ + 40³ and 31³ + 33³).
- 2
65728 is composite. Its prime factorisation is
- 3
The divisors add up to 142240; without 65728 itself that is 76512, so 65728 is abundant (76512 is more than 65728). Euler's totient φ(65728) = 29952 numbers up to 65728 share no factor with it.
- 4
The digits of 65728 add up to 28, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 65728 = 2^{6} \times 13 \times 79 \]65728 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 142240 |
| Euler totient φ(n) | 29952 |
| Square | 4320169984 |
| Cube | 283956132708352 |
| Square root | 256.374726 (= 8√1027) |
| Digit sum / digital root | 28 / 1 |
| Collatz steps to 1 | 42 |
| Scientific notation | 6.5728 × |
65728 in other forms
| Form | Value |
|---|---|
| In words | sixty-five thousand seven hundred and twenty-eight |
| Binary (base 2) | 10000000011000000 |
| Octal (base 8) | 200300 |
| Hexadecimal (base 16) | 100C0 |
| Base 3 | 10100011101 |
| As time | 65728 seconds = 18 h 15 min 28 s |
Is 65728 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (65728 ÷ 2 = 32864) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (65728 ÷ 4 = 16432) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (65728 ÷ 8 = 8216) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 65728 a prime number?
No. 65728 = × 13 × 79, so it is divisible by 2.
What are the factors of 65728?
1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 79, 104, 158, 208, 316, 416, 632, 832, 1027, 1264, 2054, 2528, 4108, 5056, 8216, 16432, 32864, 65728.
What is 65728 in binary?
10000000011000000 (hexadecimal 100C0, octal 200300).
What is the square root of 65728?
About 256.3747, exactly 8√1027.
Is 65728 divisible by 3?
No. Its digits add up to 28, which is not a multiple of 3.
What is special about the number 65728?
65728 is a taxicab number: it is the sum of two cubes in 2 ways (12³ + 40³ and 31³ + 33³).