Number dictionary · Exact arithmetic
882: factors and number facts
eight hundred eighty-two is an even number and is composite. Its 18 positive divisors form 9 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- eight hundred eighty-two
- Roman numeral
- DCCCLXXXII
- Prime factorization
- 2 × 3^2 × 7^2
- Digital root
- 9
All factors of 882
A positive factor divides 882 with no remainder. In ascending order, the complete list is:
1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441, 882
Factor pairs
- 1 × 882 = 882
- 2 × 441 = 882
- 3 × 294 = 882
- 6 × 147 = 882
- 7 × 126 = 882
- 9 × 98 = 882
- 14 × 63 = 882
- 18 × 49 = 882
- 21 × 42 = 882
Each pair describes an arrangement of 882 items into equal rows. The pairs have different row and column counts; 882 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 18
- Sum of all divisors
- 2223
- Sum excluding 882
- 1341
- Classification
- abundant
882 is abundant because its proper divisors add to 1341, which is greater than 882.
Prime factorization of 882
882 = 2 × 3^2 × 7^2
Repeated division, step by step
- 882 ÷ 2 = 441
- 441 ÷ 3 = 147
- 147 ÷ 3 = 49
- 49 ÷ 7 = 7
- 7 ÷ 7 = 1
Multiply the prime divisors in these steps to reconstruct 882. An exponent records how many times the same prime occurs. The divisor-count calculation is (1 + 1) × (2 + 1) × (2 + 1) = 18.
The preceding prime is 881. The next larger prime is 883. The factor list above explains why 882 is composite.
Learn the factorization method882 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | eight hundred eighty-two |
| Roman numeral | DCCCLXXXII |
| Binary (base 2) | 1101110010 |
| Octal (base 8) | 1562 |
| Decimal (base 10) | 882 |
| Hexadecimal (base 16) | 372 |
Check the binary conversion
Read 1101110010 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 + 64 + 32 + 16 + 2 = 882
Check the hexadecimal conversion
3 × 16^2 + 7 × 16^1 + 2 × 16^0 = 882
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 882
- 882 squared
- 882 × 882 = 777,924
- 882 cubed
- 882 × 882 × 882 = 686,128,968
- Square root
- ≈ 29.698485
- Simplified radical
- 21√2
882 lies between 841 (29²) and 900 (30²), so it is not a perfect square. It is not a perfect cube.
882 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 882.
Distinguish a square from a square rootMultiplication table for 882
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 | 441 | 0 | Yes |
| 3 | 294 | 0 | Yes |
| 4 | 220 | 2 | No |
| 5 | 176 | 2 | No |
| 6 | 147 | 0 | Yes |
| 7 | 126 | 0 | Yes |
| 8 | 110 | 2 | No |
| 9 | 98 | 0 | Yes |
| 10 | 88 | 2 | No |
| 11 | 80 | 2 | No |
| 12 | 73 | 6 | No |
For example, 882 = 7 × 126 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 882
882 contains 3 decimal digits. Its digit sum is 8 + 8 + 2 = 18.
- 882: 8 + 8 + 2 = 18
- 18: 1 + 8 = 9
The digital root is 9. Reversing its digits gives 288; 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, 882/100 simplifies to 441/50 by dividing both terms by their greatest common divisor, 2. Its decimal value is 8.82. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 882 and 12 is 6. Their least common multiple is 1764. The identity GCD × LCM = 882 × 12 = 10584 checks both results.
Work through GCF and LCMQuestions about 882
What are the factors of 882?
The positive factors are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441, 882. There are 18 factors, including 1 and 882.
Is 882 a prime number?
No. 882 is composite: 2 × 3^2 × 7^2 = 882.
How do you write 882 in Roman numerals?
882 is DCCCLXXXII in standard subtractive Roman numeral notation.
What is the binary representation of 882?
882 in decimal is 1101110010 in base 2. Adding its active place values gives 512 + 256 + 64 + 32 + 16 + 2 = 882.
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 882
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 882 add to 18. 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.