The number 2010
2010 is a composite number with 16 divisors. Its prime factorisation is 2 × 3 × 5 × 67. Divisors (16): 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2010: a Harshad number: divisible by its digit sum 3.
- 2
2010 is composite. Its prime factorisation is
- 3
The divisors add up to 4896; without 2010 itself that is 2886, so 2010 is abundant (2886 is more than 2010). Euler's totient φ(2010) = 528 numbers up to 2010 share no factor with it.
- 4
The digits of 2010 add up to 3, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2010 = 2 \times 3 \times 5 \times 67 \]
2010 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 4896 |
| Euler totient φ(n) | 528 |
| Square | 4040100 |
| Cube | 8120601000 |
| Square root | 44.833024 |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 68 |
| Scientific notation | 2.01 × |
2010 in other forms
| Form | Value |
|---|---|
| In words | two thousand and ten |
| Roman numerals | MMX |
| Binary (base 2) | 11111011010 |
| Octal (base 8) | 3732 |
| Hexadecimal (base 16) | 7DA |
| Base 3 | 2202110 |
| As time | 2010 seconds = 33 min 30 s |
Is 2010 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2010 ÷ 2 = 1005) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2010 ÷ 3 = 670) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (2010 ÷ 5 = 402) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (2010 ÷ 6 = 335) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (2010 ÷ 10 = 201) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2010 a prime number?
No. 2010 = 2 × 3 × 5 × 67, so it is divisible by 2.
What are the factors of 2010?
1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010.
What is 2010 in binary?
11111011010 (hexadecimal 7DA, octal 3732).
What is the square root of 2010?
About 44.8330.
What is 2010 in Roman numerals?
MMX.
Is 2010 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 2010?
2010 is a Harshad number: divisible by its digit sum 3.