Number dictionary · Exact arithmetic
1004: factors and number facts
one thousand four is an even number and is composite. Its 6 positive divisors form 3 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- one thousand four
- Roman numeral
- MIV
- Prime factorization
- 2^2 × 251
- Digital root
- 5
All factors of 1004
A positive factor divides 1004 with no remainder. In ascending order, the complete list is:
1, 2, 4, 251, 502, 1004
Factor pairs
- 1 × 1004 = 1004
- 2 × 502 = 1004
- 4 × 251 = 1004
Each pair describes an arrangement of 1004 items into equal rows. The pairs have different row and column counts; 1004 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 6
- Sum of all divisors
- 1764
- Sum excluding 1004
- 760
- Classification
- deficient
1004 is deficient because its proper divisors add to 760, which is less than 1004.
Prime factorization of 1004
1004 = 2^2 × 251
Repeated division, step by step
- 1004 ÷ 2 = 502
- 502 ÷ 2 = 251
- 251 ÷ 251 = 1
Multiply the prime divisors in these steps to reconstruct 1004. An exponent records how many times the same prime occurs. The divisor-count calculation is (2 + 1) × (1 + 1) = 6.
The preceding prime is 997. The next larger prime is 1009. The factor list above explains why 1004 is composite.
Learn the factorization method1004 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one thousand four |
| Roman numeral | MIV |
| Binary (base 2) | 1111101100 |
| Octal (base 8) | 1754 |
| Decimal (base 10) | 1004 |
| Hexadecimal (base 16) | 3EC |
Check the binary conversion
Read 1111101100 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
512 + 256 + 128 + 64 + 32 + 8 + 4 = 1004
Check the hexadecimal conversion
3 × 16^2 + 14 × 16^1 + 12 × 16^0 = 1004
Hexadecimal uses A through F for digit values 10 through 15. These notations represent the same quantity; changing the base does not change the integer.
Square, cube and square root of 1004
- 1004 squared
- 1004 × 1004 = 1,008,016
- 1004 cubed
- 1004 × 1004 × 1004 = 1,012,048,064
- Square root
- ≈ 31.685959
- Simplified radical
- 2√251
1004 lies between 961 (31²) and 1024 (32²), so it is not a perfect square. It is not a perfect cube.
1004 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 1004.
Distinguish a square from a square rootMultiplication table for 1004
These are the first twelve positive multiples. Unlike the finite factor list, the sequence of multiples continues without an upper limit.
Divisibility checks
| Divide by | Whole quotient | Remainder | Divides exactly? |
|---|---|---|---|
| 2 | 502 | 0 | Yes |
| 3 | 334 | 2 | No |
| 4 | 251 | 0 | Yes |
| 5 | 200 | 4 | No |
| 6 | 167 | 2 | No |
| 7 | 143 | 3 | No |
| 8 | 125 | 4 | No |
| 9 | 111 | 5 | No |
| 10 | 100 | 4 | No |
| 11 | 91 | 3 | No |
| 12 | 83 | 8 | No |
For example, 1004 = 7 × 143 + 3. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 1004
1004 contains 4 decimal digits. Its digit sum is 1 + 0 + 0 + 4 = 5.
- 1004: 1 + 0 + 0 + 4 = 5
The digital root is 5. Reversing its digits gives 4001; it is not a decimal palindrome. Digit patterns depend on the notation being used.
Digital-root arithmetic always finishes at a single digit for a positive integer. Some numerology methods stop at 11, 22 or 33 instead; that is a separate interpretive convention.
Fractions and a worked comparison
As a fraction of 100, 1004/100 simplifies to 251/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 10.04. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 1004 and 12 is 4. Their least common multiple is 3012. The identity GCD × LCM = 1004 × 12 = 12048 checks both results.
Work through GCF and LCMQuestions about 1004
What are the factors of 1004?
The positive factors are 1, 2, 4, 251, 502, 1004. There are 6 factors, including 1 and 1004.
Is 1004 a prime number?
No. 1004 is composite: 2^2 × 251 = 1004.
How do you write 1004 in Roman numerals?
1004 is MIV in standard subtractive Roman numeral notation.
What is the binary representation of 1004?
1004 in decimal is 1111101100 in base 2. Adding its active place values gives 512 + 256 + 128 + 64 + 32 + 8 + 4 = 1004.
Methods and reference definitions
Number JD calculates each result from the integer on this page. Positive factors are enumerated in pairs; repeated division gives the prime factorization; place values verify base conversions. Decimal square roots are rounded to six places when irrational.
NUMBER JOURNAL / JD
A reflective note on 1004
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 1004 add to 5. That arithmetic result is separate from the cultural symbolism of the pattern. If this number matters to you, write down what you noticed and choose one grounded action rather than treating the sighting as a prediction.