The number 17
17 is a twin prime (17 and 19 are both prime), the 7th prime number and a binary palindrome (10001). Its only divisors are 1 and 17.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 17: a twin prime (17 and 19 are both prime); the 7th prime number; a binary palindrome (10001).
- 2
17 is prime, so its only factors are 1 and 17. It is the 7th prime; the next prime is 19 and the one before is 13.
- 3
The divisors add up to 18; without 17 itself that is 1, so 17 is deficient (1 is less than 17). Euler's totient φ(17) = 16 numbers up to 17 share no factor with it.
- 4
The digits of 17 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 12 steps to reach 1.
17 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 18 |
| Euler totient φ(n) | 16 |
| Square | 289 |
| Cube | 4913 |
| Square root | 4.123106 |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 12 |
| Scientific notation | 1.7 × |
17 in other forms
| Form | Value |
|---|---|
| In words | seventeen |
| Roman numerals | XVII |
| Binary (base 2) | 10001 |
| Octal (base 8) | 21 |
| Hexadecimal (base 16) | 11 |
| Base 3 | 122 |
| As time | 17 seconds |
Is 17 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 6) | 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 17 a prime number?
Yes. 17 is divisible only by 1 and itself.
What are the factors of 17?
1, 17.
What is 17 in binary?
10001 (hexadecimal 11, octal 21).
What is the square root of 17?
About 4.1231.
What is 17 in Roman numerals?
XVII.
Is 17 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 17?
17 is a twin prime (17 and 19 are both prime); the 7th prime number; a binary palindrome (10001).