The number 617
617 is a twin prime (617 and 619 are both prime) and the 113th prime number. Its only divisors are 1 and 617.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 617: a twin prime (617 and 619 are both prime); the 113th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
617 is prime, so its only factors are 1 and 617. It is the 113th prime; the next prime is 619 and the one before is 613.
- 3
The divisors add up to 618; without 617 itself that is 1, so 617 is deficient (1 is less than 617). Euler's totient φ(617) = 616 numbers up to 617 share no factor with it.
- 4
The digits of 617 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 131 steps to reach 1.
617 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 618 |
| Euler totient φ(n) | 616 |
| Square | 380689 |
| Cube | 234885113 |
| Square root | 24.839485 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 131 |
| Scientific notation | 6.17 × |
617 in other forms
| Form | Value |
|---|---|
| In words | six hundred and seventeen |
| Roman numerals | DCXVII |
| Binary (base 2) | 1001101001 |
| Octal (base 8) | 1151 |
| Hexadecimal (base 16) | 269 |
| Base 3 | 211212 |
| As time | 617 seconds = 10 min 17 s |
Is 617 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 1) | 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 5) | 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 1) | 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 617 a prime number?
Yes. 617 is divisible only by 1 and itself.
What are the factors of 617?
1, 617.
What is 617 in binary?
1001101001 (hexadecimal 269, octal 1151).
What is the square root of 617?
About 24.8395.
What is 617 in Roman numerals?
DCXVII.
Is 617 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 617?
617 is a twin prime (617 and 619 are both prime); the 113th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.