Number dictionary · Exact arithmetic
1001: factors and number facts
one thousand one 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
- Roman numeral
- MI
- Prime factorization
- 7 × 11 × 13
- Digital root
- 2
All factors of 1001
A positive factor divides 1001 with no remainder. In ascending order, the complete list is:
1, 7, 11, 13, 77, 91, 143, 1001
Factor pairs
- 1 × 1001 = 1001
- 7 × 143 = 1001
- 11 × 91 = 1001
- 13 × 77 = 1001
Each pair describes an arrangement of 1001 items into equal rows. The pairs have different row and column counts; 1001 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 8
- Sum of all divisors
- 1344
- Sum excluding 1001
- 343
- Classification
- deficient
1001 is deficient because its proper divisors add to 343, which is less than 1001.
Prime factorization of 1001
1001 = 7 × 11 × 13
Repeated division, step by step
- 1001 ÷ 7 = 143
- 143 ÷ 11 = 13
- 13 ÷ 13 = 1
Multiply the prime divisors in these steps to reconstruct 1001. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) × (1 + 1) = 8.
The preceding prime is 997. The next larger prime is 1009. The factor list above explains why 1001 is composite.
Learn the factorization method1001 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one thousand one |
| Roman numeral | MI |
| Binary (base 2) | 1111101001 |
| Octal (base 8) | 1751 |
| Decimal (base 10) | 1001 |
| Hexadecimal (base 16) | 3E9 |
Check the binary conversion
Read 1111101001 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 + 1 = 1001
Check the hexadecimal conversion
3 × 16^2 + 14 × 16^1 + 9 × 16^0 = 1001
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 1001
- 1001 squared
- 1001 × 1001 = 1,002,001
- 1001 cubed
- 1001 × 1001 × 1001 = 1,003,003,001
- Square root
- ≈ 31.638584
- Simplified radical
- √1001
1001 lies between 961 (31²) and 1024 (32²), so it is not a perfect square. It is not a perfect cube.
1001 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 1001.
Distinguish a square from a square rootMultiplication table for 1001
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 | 500 | 1 | No |
| 3 | 333 | 2 | No |
| 4 | 250 | 1 | No |
| 5 | 200 | 1 | No |
| 6 | 166 | 5 | No |
| 7 | 143 | 0 | Yes |
| 8 | 125 | 1 | No |
| 9 | 111 | 2 | No |
| 10 | 100 | 1 | No |
| 11 | 91 | 0 | Yes |
| 12 | 83 | 5 | No |
For example, 1001 = 7 × 143 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 1001
1001 contains 4 decimal digits. Its digit sum is 1 + 0 + 0 + 1 = 2.
- 1001: 1 + 0 + 0 + 1 = 2
The digital root is 2. 1001 reads the same forward and backward, making it 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, 1001/100 simplifies to 1001/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 10.01. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 1001 and 12 is 1. Their least common multiple is 12012. The identity GCD × LCM = 1001 × 12 = 12012 checks both results.
Work through GCF and LCMQuestions about 1001
What are the factors of 1001?
The positive factors are 1, 7, 11, 13, 77, 91, 143, 1001. There are 8 factors, including 1 and 1001.
Is 1001 a prime number?
No. 1001 is composite: 7 × 11 × 13 = 1001.
How do you write 1001 in Roman numerals?
1001 is MI in standard subtractive Roman numeral notation.
What is the binary representation of 1001?
1001 in decimal is 1111101001 in base 2. Adding its active place values gives 512 + 256 + 128 + 64 + 32 + 8 + 1 = 1001.
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 1001
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 1001 add to 2. 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.