The number 2013
2013 is a composite number with 8 divisors. Its prime factorisation is 3 × 11 × 61. Divisors (8): 1, 3, 11, 33, 61, 183, 671, 2013.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
2013 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
2013 is composite. Its prime factorisation is
- 3
The divisors add up to 2976; without 2013 itself that is 963, so 2013 is deficient (963 is less than 2013). Euler's totient φ(2013) = 1200 numbers up to 2013 share no factor with it.
- 4
The digits of 2013 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2013 = 3 \times 11 \times 61 \]
2013 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 2976 |
| Euler totient φ(n) | 1200 |
| Square | 4052169 |
| Cube | 8157016197 |
| Square root | 44.866469 |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 68 |
| Scientific notation | 2.013 × |
2013 in other forms
| Form | Value |
|---|---|
| In words | two thousand and thirteen |
| Roman numerals | MMXIII |
| Binary (base 2) | 11111011101 |
| Octal (base 8) | 3735 |
| Hexadecimal (base 16) | 7DD |
| Base 3 | 2202120 |
| As time | 2013 seconds = 33 min 33 s |
Is 2013 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 (2013 ÷ 3 = 671) | 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 3) | 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 4) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (2013 ÷ 11 = 183) | 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 2013 a prime number?
No. 2013 = 3 × 11 × 61, so it is divisible by 3.
What are the factors of 2013?
1, 3, 11, 33, 61, 183, 671, 2013.
What is 2013 in binary?
11111011101 (hexadecimal 7DD, octal 3735).
What is the square root of 2013?
About 44.8665.
What is 2013 in Roman numerals?
MMXIII.
Is 2013 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 2013?
It is a composite number with 8 divisors.