Number dictionary · Exact arithmetic
1021: factors and number facts
one thousand twenty-one 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 twenty-one
- Roman numeral
- MXXI
- Prime factorization
- 1021
- Digital root
- 4
All factors of 1021
A positive factor divides 1021 with no remainder. In ascending order, the complete list is:
1, 1021
Factor pairs
- 1 × 1021 = 1021
Each pair describes an arrangement of 1021 items into equal rows. The pairs have different row and column counts; 1021 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 2
- Sum of all divisors
- 1022
- Sum excluding 1021
- 1
- Classification
- deficient
1021 is deficient because its proper divisors add to 1, which is less than 1021.
Prime factorization of 1021
1021 = 1021
Repeated division, step by step
- 1021 ÷ 1021 = 1
Multiply the prime divisors in these steps to reconstruct 1021. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) = 2.
The preceding prime is 1019. The next larger prime is 1031. To check 1021 for primality, it is sufficient to test possible divisors from 2 through 31.
Learn the factorization method1021 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one thousand twenty-one |
| Roman numeral | MXXI |
| Binary (base 2) | 1111111101 |
| Octal (base 8) | 1775 |
| Decimal (base 10) | 1021 |
| Hexadecimal (base 16) | 3FD |
Check the binary conversion
Read 1111111101 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 + 8 + 4 + 1 = 1021
Check the hexadecimal conversion
3 × 16^2 + 15 × 16^1 + 13 × 16^0 = 1021
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 1021
- 1021 squared
- 1021 × 1021 = 1,042,441
- 1021 cubed
- 1021 × 1021 × 1021 = 1,064,332,261
- Square root
- ≈ 31.953091
- Simplified radical
- √1021
1021 lies between 961 (31²) and 1024 (32²), so it is not a perfect square. It is not a perfect cube.
1021 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 1021.
Distinguish a square from a square rootMultiplication table for 1021
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 | 510 | 1 | No |
| 3 | 340 | 1 | No |
| 4 | 255 | 1 | No |
| 5 | 204 | 1 | No |
| 6 | 170 | 1 | No |
| 7 | 145 | 6 | No |
| 8 | 127 | 5 | No |
| 9 | 113 | 4 | No |
| 10 | 102 | 1 | No |
| 11 | 92 | 9 | No |
| 12 | 85 | 1 | No |
For example, 1021 = 7 × 145 + 6. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 1021
1021 contains 4 decimal digits. Its digit sum is 1 + 0 + 2 + 1 = 4.
- 1021: 1 + 0 + 2 + 1 = 4
The digital root is 4. Reversing its digits gives 1201; 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, 1021/100 simplifies to 1021/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 10.21. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 1021 and 12 is 1. Their least common multiple is 12252. The identity GCD × LCM = 1021 × 12 = 12252 checks both results.
Work through GCF and LCMQuestions about 1021
What are the factors of 1021?
The positive factors are 1, 1021. There are 2 factors, including 1 and 1021.
Is 1021 a prime number?
Yes. The only positive divisors of 1021 are 1 and 1021.
How do you write 1021 in Roman numerals?
1021 is MXXI in standard subtractive Roman numeral notation.
What is the binary representation of 1021?
1021 in decimal is 1111111101 in base 2. Adding its active place values gives 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 1 = 1021.
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 1021
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 1021 add to 4. 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.