The number 1017
1017 is a composite number with 6 divisors. Its prime factorisation is × 113. Divisors (6): 1, 3, 9, 113, 339, 1017.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1017: a Harshad number: divisible by its digit sum 9.
- 2
1017 is composite. Its prime factorisation is
- 3
The divisors add up to 1482; without 1017 itself that is 465, so 1017 is deficient (465 is less than 1017). Euler's totient φ(1017) = 672 numbers up to 1017 share no factor with it.
- 4
The digits of 1017 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 155 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1017 = 3^{2} \times 113 \]1017 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 1482 |
| Euler totient φ(n) | 672 |
| Square | 1034289 |
| Cube | 1051871913 |
| Square root | 31.890437 (= 3√113) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 155 |
| Scientific notation | 1.017 × |
1017 in other forms
| Form | Value |
|---|---|
| In words | one thousand and seventeen |
| Roman numerals | MXVII |
| Binary (base 2) | 1111111001 |
| Octal (base 8) | 1771 |
| Hexadecimal (base 16) | 3F9 |
| Base 3 | 1101200 |
| As time | 1017 seconds = 16 min 57 s |
Is 1017 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 | Yes (1017 ÷ 3 = 339) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | Yes (1017 ÷ 9 = 113) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1017 a prime number?
No. 1017 = × 113, so it is divisible by 3.
What are the factors of 1017?
1, 3, 9, 113, 339, 1017.
What is 1017 in binary?
1111111001 (hexadecimal 3F9, octal 1771).
What is the square root of 1017?
About 31.8904, exactly 3√113.
What is 1017 in Roman numerals?
MXVII.
Is 1017 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1017?
1017 is a Harshad number: divisible by its digit sum 9.