The number 65736
65736 is a composite number with 48 divisors. Its prime factorisation is × × 11 × 83. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 44, 66 … 65736.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
65736 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
65736 is composite. Its prime factorisation is
- 3
The divisors add up to 196560; without 65736 itself that is 130824, so 65736 is abundant (130824 is more than 65736). Euler's totient φ(65736) = 19680 numbers up to 65736 share no factor with it.
- 4
The digits of 65736 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 161 steps to reach 1.
LaTeX source of the formulas on this page
\[ 65736 = 2^{3} \times 3^{2} \times 11 \times 83 \]65736 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 196560 |
| Euler totient φ(n) | 19680 |
| Square | 4321221696 |
| Cube | 284059829408256 |
| Square root | 256.390327 (= 6√1826) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 161 |
| Scientific notation | 6.5736 × |
65736 in other forms
| Form | Value |
|---|---|
| In words | sixty-five thousand seven hundred and thirty-six |
| Binary (base 2) | 10000000011001000 |
| Octal (base 8) | 200310 |
| Hexadecimal (base 16) | 100C8 |
| Base 3 | 10100011200 |
| As time | 65736 seconds = 18 h 15 min 36 s |
Is 65736 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (65736 ÷ 2 = 32868) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (65736 ÷ 3 = 21912) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (65736 ÷ 4 = 16434) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (65736 ÷ 6 = 10956) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (65736 ÷ 8 = 8217) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (65736 ÷ 9 = 7304) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (65736 ÷ 11 = 5976) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (65736 ÷ 12 = 5478) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 65736 a prime number?
No. 65736 = × × 11 × 83, so it is divisible by 2.
What are the factors of 65736?
1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 83, 88, 99, 132, 166, 198, 249, 264, 332, 396, 498, 664, 747, 792, 913, 996, 1494, 1826, 1992, 2739, 2988, 3652, 5478, 5976, 7304, 8217, 10956, 16434, 21912, 32868, 65736.
What is 65736 in binary?
10000000011001000 (hexadecimal 100C8, octal 200310).
What is the square root of 65736?
About 256.3903, exactly 6√1826.
Is 65736 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 65736?
It is a composite number with 48 divisors.