The number 65537
65537 is a twin prime (65537 and 65539 are both prime), the 6543rd prime number and a binary palindrome (10000000000000001). Its only divisors are 1 and 65537.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 65537: a twin prime (65537 and 65539 are both prime); the 6543rd prime number; a binary palindrome (10000000000000001).
- 2
65537 is prime, so its only factors are 1 and 65537. It is the 6543rd prime; the next prime is 65539 and the one before is 65521.
- 3
The divisors add up to 65538; without 65537 itself that is 1, so 65537 is deficient (1 is less than 65537). Euler's totient φ(65537) = 65536 numbers up to 65537 share no factor with it.
- 4
The digits of 65537 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 99 steps to reach 1.
65537 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 65538 |
| Euler totient φ(n) | 65536 |
| Square | 4295098369 |
| Cube | 281487861809153 |
| Square root | 256.001953 |
| Digit sum / digital root | 26 / 8 |
| Collatz steps to 1 | 99 |
| Scientific notation | 6.5537 × |
65537 in other forms
| Form | Value |
|---|---|
| In words | sixty-five thousand five hundred and thirty-seven |
| Binary (base 2) | 10000000000000001 |
| Octal (base 8) | 200001 |
| Hexadecimal (base 16) | 10001 |
| Base 3 | 10022220022 |
| As time | 65537 seconds = 18 h 12 min 17 s |
Is 65537 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 65537 a prime number?
Yes. 65537 is divisible only by 1 and itself.
What are the factors of 65537?
1, 65537.
What is 65537 in binary?
10000000000000001 (hexadecimal 10001, octal 200001).
What is the square root of 65537?
About 256.0020.
Is 65537 divisible by 3?
No. Its digits add up to 26, which is not a multiple of 3.
What is special about the number 65537?
65537 is a twin prime (65537 and 65539 are both prime); the 6543rd prime number; a binary palindrome (10000000000000001).