Number dictionary · Exact arithmetic
1104: factors and number facts
one thousand one hundred four is an even number and is composite. Its 20 positive divisors form 10 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- one thousand one hundred four
- Roman numeral
- MCIV
- Prime factorization
- 2^4 × 3 × 23
- Digital root
- 6
All factors of 1104
A positive factor divides 1104 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 46, 48, 69, 92, 138, 184, 276, 368, 552, 1104
Factor pairs
- 1 × 1104 = 1104
- 2 × 552 = 1104
- 3 × 368 = 1104
- 4 × 276 = 1104
- 6 × 184 = 1104
- 8 × 138 = 1104
- 12 × 92 = 1104
- 16 × 69 = 1104
- 23 × 48 = 1104
- 24 × 46 = 1104
Each pair describes an arrangement of 1104 items into equal rows. The pairs have different row and column counts; 1104 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 20
- Sum of all divisors
- 2976
- Sum excluding 1104
- 1872
- Classification
- abundant
1104 is abundant because its proper divisors add to 1872, which is greater than 1104.
Prime factorization of 1104
1104 = 2^4 × 3 × 23
Repeated division, step by step
- 1104 ÷ 2 = 552
- 552 ÷ 2 = 276
- 276 ÷ 2 = 138
- 138 ÷ 2 = 69
- 69 ÷ 3 = 23
- 23 ÷ 23 = 1
Multiply the prime divisors in these steps to reconstruct 1104. An exponent records how many times the same prime occurs. The divisor-count calculation is (4 + 1) × (1 + 1) × (1 + 1) = 20.
The preceding prime is 1103. The next larger prime is 1109. The factor list above explains why 1104 is composite.
Learn the factorization method1104 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one thousand one hundred four |
| Roman numeral | MCIV |
| Binary (base 2) | 10001010000 |
| Octal (base 8) | 2120 |
| Decimal (base 10) | 1104 |
| Hexadecimal (base 16) | 450 |
Check the binary conversion
Read 10001010000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
1024 + 64 + 16 = 1104
Check the hexadecimal conversion
4 × 16^2 + 5 × 16^1 + 0 × 16^0 = 1104
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 1104
- 1104 squared
- 1104 × 1104 = 1,218,816
- 1104 cubed
- 1104 × 1104 × 1104 = 1,345,572,864
- Square root
- ≈ 33.226495
- Simplified radical
- 4√69
1104 lies between 1089 (33²) and 1156 (34²), so it is not a perfect square. It is not a perfect cube.
1104 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 1104.
Distinguish a square from a square rootMultiplication table for 1104
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 | 552 | 0 | Yes |
| 3 | 368 | 0 | Yes |
| 4 | 276 | 0 | Yes |
| 5 | 220 | 4 | No |
| 6 | 184 | 0 | Yes |
| 7 | 157 | 5 | No |
| 8 | 138 | 0 | Yes |
| 9 | 122 | 6 | No |
| 10 | 110 | 4 | No |
| 11 | 100 | 4 | No |
| 12 | 92 | 0 | Yes |
For example, 1104 = 7 × 157 + 5. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 1104
1104 contains 4 decimal digits. Its digit sum is 1 + 1 + 0 + 4 = 6.
- 1104: 1 + 1 + 0 + 4 = 6
The digital root is 6. Reversing its digits gives 4011; 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, 1104/100 simplifies to 276/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 11.04. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 1104 and 12 is 12. Their least common multiple is 1104. The identity GCD × LCM = 1104 × 12 = 13248 checks both results.
Work through GCF and LCMQuestions about 1104
What are the factors of 1104?
The positive factors are 1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 46, 48, 69, 92, 138, 184, 276, 368, 552, 1104. There are 20 factors, including 1 and 1104.
Is 1104 a prime number?
No. 1104 is composite: 2^4 × 3 × 23 = 1104.
How do you write 1104 in Roman numerals?
1104 is MCIV in standard subtractive Roman numeral notation.
What is the binary representation of 1104?
1104 in decimal is 10001010000 in base 2. Adding its active place values gives 1024 + 64 + 16 = 1104.
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 1104
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 1104 add to 6. 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.