Number dictionary · Exact arithmetic
1009: factors and number facts
one thousand nine is an odd number and is prime. Its 2 positive divisors form 1 factor pair.
Number JD Editorial Team · Updated 2026-10-08
- In words
- one thousand nine
- Roman numeral
- MIX
- Prime factorization
- 1009
- Digital root
- 1
All factors of 1009
A positive factor divides 1009 with no remainder. In ascending order, the complete list is:
1, 1009
Factor pairs
- 1 × 1009 = 1009
Each pair describes an arrangement of 1009 items into equal rows. The pairs have different row and column counts; 1009 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 2
- Sum of all divisors
- 1010
- Sum excluding 1009
- 1
- Classification
- deficient
1009 is deficient because its proper divisors add to 1, which is less than 1009.
Prime factorization of 1009
1009 = 1009
Repeated division, step by step
- 1009 ÷ 1009 = 1
Multiply the prime divisors in these steps to reconstruct 1009. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) = 2.
The preceding prime is 997. The next larger prime is 1013. To check 1009 for primality, it is sufficient to test possible divisors from 2 through 31.
Learn the factorization method1009 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one thousand nine |
| Roman numeral | MIX |
| Binary (base 2) | 1111110001 |
| Octal (base 8) | 1761 |
| Decimal (base 10) | 1009 |
| Hexadecimal (base 16) | 3F1 |
Check the binary conversion
Read 1111110001 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 + 16 + 1 = 1009
Check the hexadecimal conversion
3 × 16^2 + 15 × 16^1 + 1 × 16^0 = 1009
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 1009
- 1009 squared
- 1009 × 1009 = 1,018,081
- 1009 cubed
- 1009 × 1009 × 1009 = 1,027,243,729
- Square root
- ≈ 31.764760
- Simplified radical
- √1009
1009 lies between 961 (31²) and 1024 (32²), so it is not a perfect square. It is not a perfect cube.
1009 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 1009.
Distinguish a square from a square rootMultiplication table for 1009
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 | 504 | 1 | No |
| 3 | 336 | 1 | No |
| 4 | 252 | 1 | No |
| 5 | 201 | 4 | No |
| 6 | 168 | 1 | No |
| 7 | 144 | 1 | No |
| 8 | 126 | 1 | No |
| 9 | 112 | 1 | No |
| 10 | 100 | 9 | No |
| 11 | 91 | 8 | No |
| 12 | 84 | 1 | No |
For example, 1009 = 7 × 144 + 1. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 1009
1009 contains 4 decimal digits. Its digit sum is 1 + 0 + 0 + 9 = 10.
- 1009: 1 + 0 + 0 + 9 = 10
- 10: 1 + 0 = 1
The digital root is 1. Reversing its digits gives 9001; 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, 1009/100 simplifies to 1009/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 10.09. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 1009 and 12 is 1. Their least common multiple is 12108. The identity GCD × LCM = 1009 × 12 = 12108 checks both results.
Work through GCF and LCMQuestions about 1009
What are the factors of 1009?
The positive factors are 1, 1009. There are 2 factors, including 1 and 1009.
Is 1009 a prime number?
Yes. The only positive divisors of 1009 are 1 and 1009.
How do you write 1009 in Roman numerals?
1009 is MIX in standard subtractive Roman numeral notation.
What is the binary representation of 1009?
1009 in decimal is 1111110001 in base 2. Adding its active place values gives 512 + 256 + 128 + 64 + 32 + 16 + 1 = 1009.
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 1009
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 1009 add to 10. 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.