The number 2007
2007 is a composite number with 6 divisors. Its prime factorisation is × 223. Divisors (6): 1, 3, 9, 223, 669, 2007.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2007: a Harshad number: divisible by its digit sum 9.
- 2
2007 is composite. Its prime factorisation is
- 3
The divisors add up to 2912; without 2007 itself that is 905, so 2007 is deficient (905 is less than 2007). Euler's totient φ(2007) = 1332 numbers up to 2007 share no factor with it.
- 4
The digits of 2007 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 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2007 = 3^{2} \times 223 \]2007 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 2912 |
| Euler totient φ(n) | 1332 |
| Square | 4028049 |
| Cube | 8084294343 |
| Square root | 44.799554 (= 3√223) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 42 |
| Scientific notation | 2.007 × |
2007 in other forms
| Form | Value |
|---|---|
| In words | two thousand and seven |
| Roman numerals | MMVII |
| Binary (base 2) | 11111010111 |
| Octal (base 8) | 3727 |
| Hexadecimal (base 16) | 7D7 |
| Base 3 | 2202100 |
| As time | 2007 seconds = 33 min 27 s |
Is 2007 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 (2007 ÷ 3 = 669) | 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 | 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 5) | 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 | Yes (2007 ÷ 9 = 223) | 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 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2007 a prime number?
No. 2007 = × 223, so it is divisible by 3.
What are the factors of 2007?
1, 3, 9, 223, 669, 2007.
What is 2007 in binary?
11111010111 (hexadecimal 7D7, octal 3727).
What is the square root of 2007?
About 44.7996, exactly 3√223.
What is 2007 in Roman numerals?
MMVII.
Is 2007 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 2007?
2007 is a Harshad number: divisible by its digit sum 9.