The number 2008
2008 is a composite number with 8 divisors. Its prime factorisation is × 251. Divisors (8): 1, 2, 4, 8, 251, 502, 1004, 2008.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2008: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
2008 is composite. Its prime factorisation is
- 3
The divisors add up to 3780; without 2008 itself that is 1772, so 2008 is deficient (1772 is less than 2008). Euler's totient φ(2008) = 1000 numbers up to 2008 share no factor with it.
- 4
The digits of 2008 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2008 = 2^{3} \times 251 \]2008 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 3780 |
| Euler totient φ(n) | 1000 |
| Square | 4032064 |
| Cube | 8096384512 |
| Square root | 44.810713 (= 2√502) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 68 |
| Scientific notation | 2.008 × |
2008 in other forms
| Form | Value |
|---|---|
| In words | two thousand and eight |
| Roman numerals | MMVIII |
| Binary (base 2) | 11111011000 |
| Octal (base 8) | 3730 |
| Hexadecimal (base 16) | 7D8 |
| Base 3 | 2202101 |
| As time | 2008 seconds = 33 min 28 s |
Is 2008 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2008 ÷ 2 = 1004) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2008 ÷ 4 = 502) | 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 4) | 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 | Yes (2008 ÷ 8 = 251) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2008 a prime number?
No. 2008 = × 251, so it is divisible by 2.
What are the factors of 2008?
1, 2, 4, 8, 251, 502, 1004, 2008.
What is 2008 in binary?
11111011000 (hexadecimal 7D8, octal 3730).
What is the square root of 2008?
About 44.8107, exactly 2√502.
What is 2008 in Roman numerals?
MMVIII.
Is 2008 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 2008?
2008 is a happy number: repeatedly adding the squares of its digits reaches 1.