The number 1004
1004 is a composite number with 6 divisors. Its prime factorisation is × 251. Divisors (6): 1, 2, 4, 251, 502, 1004.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1004 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1004 is composite. Its prime factorisation is
- 3
The divisors add up to 1764; without 1004 itself that is 760, so 1004 is deficient (760 is less than 1004). Euler's totient φ(1004) = 500 numbers up to 1004 share no factor with it.
- 4
The digits of 1004 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 67 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1004 = 2^{2} \times 251 \]1004 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 1764 |
| Euler totient φ(n) | 500 |
| Square | 1008016 |
| Cube | 1012048064 |
| Square root | 31.685959 (= 2√251) |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 67 |
| Scientific notation | 1.004 × |
1004 in other forms
| Form | Value |
|---|---|
| In words | one thousand and four |
| Roman numerals | MIV |
| Binary (base 2) | 1111101100 |
| Octal (base 8) | 1754 |
| Hexadecimal (base 16) | 3EC |
| Base 3 | 1101012 |
| As time | 1004 seconds = 16 min 44 s |
Is 1004 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1004 ÷ 2 = 502) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1004 ÷ 4 = 251) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 5) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1004 a prime number?
No. 1004 = × 251, so it is divisible by 2.
What are the factors of 1004?
1, 2, 4, 251, 502, 1004.
What is 1004 in binary?
1111101100 (hexadecimal 3EC, octal 1754).
What is the square root of 1004?
About 31.6860, exactly 2√251.
What is 1004 in Roman numerals?
MIV.
Is 1004 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 1004?
It is a composite number with 6 divisors.