The number 2017
2017 is the 306th prime number. Its only divisors are 1 and 2017.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2017: the 306th prime number.
- 2
2017 is prime, so its only factors are 1 and 2017. It is the 306th prime; the next prime is 2027 and the one before is 2011.
- 3
The divisors add up to 2018; without 2017 itself that is 1, so 2017 is deficient (1 is less than 2017). Euler's totient φ(2017) = 2016 numbers up to 2017 share no factor with it.
- 4
The digits of 2017 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
2017 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 2018 |
| Euler totient φ(n) | 2016 |
| Square | 4068289 |
| Cube | 8205738913 |
| Square root | 44.911023 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 68 |
| Scientific notation | 2.017 × |
2017 in other forms
| Form | Value |
|---|---|
| In words | two thousand and seventeen |
| Roman numerals | MMXVII |
| Binary (base 2) | 11111100001 |
| Octal (base 8) | 3741 |
| Hexadecimal (base 16) | 7E1 |
| Base 3 | 2202201 |
| As time | 2017 seconds = 33 min 37 s |
Is 2017 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 1) | 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 1) | 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 1) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2017 a prime number?
Yes. 2017 is divisible only by 1 and itself.
What are the factors of 2017?
1, 2017.
What is 2017 in binary?
11111100001 (hexadecimal 7E1, octal 3741).
What is the square root of 2017?
About 44.9110.
What is 2017 in Roman numerals?
MMXVII.
Is 2017 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 2017?
2017 is the 306th prime number.