Number dictionary · Exact arithmetic
1107: factors and number facts
one thousand one hundred seven is an odd number and is composite. Its 8 positive divisors form 4 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- one thousand one hundred seven
- Roman numeral
- MCVII
- Prime factorization
- 3^3 × 41
- Digital root
- 9
All factors of 1107
A positive factor divides 1107 with no remainder. In ascending order, the complete list is:
1, 3, 9, 27, 41, 123, 369, 1107
Factor pairs
- 1 × 1107 = 1107
- 3 × 369 = 1107
- 9 × 123 = 1107
- 27 × 41 = 1107
Each pair describes an arrangement of 1107 items into equal rows. The pairs have different row and column counts; 1107 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 8
- Sum of all divisors
- 1680
- Sum excluding 1107
- 573
- Classification
- deficient
1107 is deficient because its proper divisors add to 573, which is less than 1107.
Prime factorization of 1107
1107 = 3^3 × 41
Repeated division, step by step
- 1107 ÷ 3 = 369
- 369 ÷ 3 = 123
- 123 ÷ 3 = 41
- 41 ÷ 41 = 1
Multiply the prime divisors in these steps to reconstruct 1107. An exponent records how many times the same prime occurs. The divisor-count calculation is (3 + 1) × (1 + 1) = 8.
The preceding prime is 1103. The next larger prime is 1109. The factor list above explains why 1107 is composite.
Learn the factorization method1107 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one thousand one hundred seven |
| Roman numeral | MCVII |
| Binary (base 2) | 10001010011 |
| Octal (base 8) | 2123 |
| Decimal (base 10) | 1107 |
| Hexadecimal (base 16) | 453 |
Check the binary conversion
Read 10001010011 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 + 2 + 1 = 1107
Check the hexadecimal conversion
4 × 16^2 + 5 × 16^1 + 3 × 16^0 = 1107
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 1107
- 1107 squared
- 1107 × 1107 = 1,225,449
- 1107 cubed
- 1107 × 1107 × 1107 = 1,356,572,043
- Square root
- ≈ 33.271610
- Simplified radical
- 3√123
1107 lies between 1089 (33²) and 1156 (34²), so it is not a perfect square. It is not a perfect cube.
1107 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 1107.
Distinguish a square from a square rootMultiplication table for 1107
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 | 553 | 1 | No |
| 3 | 369 | 0 | Yes |
| 4 | 276 | 3 | No |
| 5 | 221 | 2 | No |
| 6 | 184 | 3 | No |
| 7 | 158 | 1 | No |
| 8 | 138 | 3 | No |
| 9 | 123 | 0 | Yes |
| 10 | 110 | 7 | No |
| 11 | 100 | 7 | No |
| 12 | 92 | 3 | No |
For example, 1107 = 7 × 158 + 1. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 1107
1107 contains 4 decimal digits. Its digit sum is 1 + 1 + 0 + 7 = 9.
- 1107: 1 + 1 + 0 + 7 = 9
The digital root is 9. Reversing its digits gives 7011; 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, 1107/100 simplifies to 1107/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 11.07. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 1107 and 12 is 3. Their least common multiple is 4428. The identity GCD × LCM = 1107 × 12 = 13284 checks both results.
Work through GCF and LCMQuestions about 1107
What are the factors of 1107?
The positive factors are 1, 3, 9, 27, 41, 123, 369, 1107. There are 8 factors, including 1 and 1107.
Is 1107 a prime number?
No. 1107 is composite: 3^3 × 41 = 1107.
How do you write 1107 in Roman numerals?
1107 is MCVII in standard subtractive Roman numeral notation.
What is the binary representation of 1107?
1107 in decimal is 10001010011 in base 2. Adding its active place values gives 1024 + 64 + 16 + 2 + 1 = 1107.
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 1107
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 1107 add to 9. 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.