The number 2015
2015 is a binary palindrome (11111011111). Its prime factorisation is 5 × 13 × 31. Divisors (8): 1, 5, 13, 31, 65, 155, 403, 2015.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2015: a binary palindrome (11111011111).
- 2
2015 is composite. Its prime factorisation is
- 3
The divisors add up to 2688; without 2015 itself that is 673, so 2015 is deficient (673 is less than 2015). Euler's totient φ(2015) = 1440 numbers up to 2015 share no factor with it.
- 4
The digits of 2015 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 94 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2015 = 5 \times 13 \times 31 \]
2015 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 2688 |
| Euler totient φ(n) | 1440 |
| Square | 4060225 |
| Cube | 8181353375 |
| Square root | 44.888751 |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 94 |
| Scientific notation | 2.015 × |
2015 in other forms
| Form | Value |
|---|---|
| In words | two thousand and fifteen |
| Roman numerals | MMXV |
| Binary (base 2) | 11111011111 |
| Octal (base 8) | 3737 |
| Hexadecimal (base 16) | 7DF |
| Base 3 | 2202122 |
| As time | 2015 seconds = 33 min 35 s |
Is 2015 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 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (2015 ÷ 5 = 403) | 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 6) | 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 7) | 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 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2015 a prime number?
No. 2015 = 5 × 13 × 31, so it is divisible by 5.
What are the factors of 2015?
1, 5, 13, 31, 65, 155, 403, 2015.
What is 2015 in binary?
11111011111 (hexadecimal 7DF, octal 3737).
What is the square root of 2015?
About 44.8888.
What is 2015 in Roman numerals?
MMXV.
Is 2015 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 2015?
2015 is a binary palindrome (11111011111).