The number 2004
2004 is a composite number with 12 divisors. Its prime factorisation is × 3 × 167. Divisors (12): 1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2004: a Harshad number: divisible by its digit sum 6.
- 2
2004 is composite. Its prime factorisation is
- 3
The divisors add up to 4704; without 2004 itself that is 2700, so 2004 is abundant (2700 is more than 2004). Euler's totient φ(2004) = 664 numbers up to 2004 share no factor with it.
- 4
The digits of 2004 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 112 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2004 = 2^{2} \times 3 \times 167 \]2004 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 4704 |
| Euler totient φ(n) | 664 |
| Square | 4016016 |
| Cube | 8048096064 |
| Square root | 44.766059 (= 2√501) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 112 |
| Scientific notation | 2.004 × |
2004 in other forms
| Form | Value |
|---|---|
| In words | two thousand and four |
| Roman numerals | MMIV |
| Binary (base 2) | 11111010100 |
| Octal (base 8) | 3724 |
| Hexadecimal (base 16) | 7D4 |
| Base 3 | 2202020 |
| As time | 2004 seconds = 33 min 24 s |
Is 2004 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2004 ÷ 2 = 1002) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2004 ÷ 3 = 668) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2004 ÷ 4 = 501) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (2004 ÷ 6 = 334) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 4) | 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 4) | 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 | Yes (2004 ÷ 12 = 167) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2004 a prime number?
No. 2004 = × 3 × 167, so it is divisible by 2.
What are the factors of 2004?
1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004.
What is 2004 in binary?
11111010100 (hexadecimal 7D4, octal 3724).
What is the square root of 2004?
About 44.7661, exactly 2√501.
What is 2004 in Roman numerals?
MMIV.
Is 2004 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 2004?
2004 is a Harshad number: divisible by its digit sum 6.