Number dictionary · Exact arithmetic
880: factors and number facts
eight hundred eighty is an even number and is composite. Its 20 positive divisors form 10 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- eight hundred eighty
- Roman numeral
- DCCCLXXX
- Prime factorization
- 2^4 × 5 × 11
- Digital root
- 7
All factors of 880
A positive factor divides 880 with no remainder. In ascending order, the complete list is:
1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440, 880
Factor pairs
- 1 × 880 = 880
- 2 × 440 = 880
- 4 × 220 = 880
- 5 × 176 = 880
- 8 × 110 = 880
- 10 × 88 = 880
- 11 × 80 = 880
- 16 × 55 = 880
- 20 × 44 = 880
- 22 × 40 = 880
Each pair describes an arrangement of 880 items into equal rows. The pairs have different row and column counts; 880 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 20
- Sum of all divisors
- 2232
- Sum excluding 880
- 1352
- Classification
- abundant
880 is abundant because its proper divisors add to 1352, which is greater than 880.
Prime factorization of 880
880 = 2^4 × 5 × 11
Repeated division, step by step
- 880 ÷ 2 = 440
- 440 ÷ 2 = 220
- 220 ÷ 2 = 110
- 110 ÷ 2 = 55
- 55 ÷ 5 = 11
- 11 ÷ 11 = 1
Multiply the prime divisors in these steps to reconstruct 880. An exponent records how many times the same prime occurs. The divisor-count calculation is (4 + 1) × (1 + 1) × (1 + 1) = 20.
The preceding prime is 877. The next larger prime is 881. The factor list above explains why 880 is composite.
Learn the factorization method880 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | eight hundred eighty |
| Roman numeral | DCCCLXXX |
| Binary (base 2) | 1101110000 |
| Octal (base 8) | 1560 |
| Decimal (base 10) | 880 |
| Hexadecimal (base 16) | 370 |
Check the binary conversion
Read 1101110000 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 = 880
Check the hexadecimal conversion
3 × 16^2 + 7 × 16^1 + 0 × 16^0 = 880
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 880
- 880 squared
- 880 × 880 = 774,400
- 880 cubed
- 880 × 880 × 880 = 681,472,000
- Square root
- ≈ 29.664794
- Simplified radical
- 4√55
880 lies between 841 (29²) and 900 (30²), so it is not a perfect square. It is not a perfect cube.
880 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 880.
Distinguish a square from a square rootMultiplication table for 880
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 | 440 | 0 | Yes |
| 3 | 293 | 1 | No |
| 4 | 220 | 0 | Yes |
| 5 | 176 | 0 | Yes |
| 6 | 146 | 4 | No |
| 7 | 125 | 5 | No |
| 8 | 110 | 0 | Yes |
| 9 | 97 | 7 | No |
| 10 | 88 | 0 | Yes |
| 11 | 80 | 0 | Yes |
| 12 | 73 | 4 | No |
For example, 880 = 7 × 125 + 5. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 880
880 contains 3 decimal digits. Its digit sum is 8 + 8 + 0 = 16.
- 880: 8 + 8 + 0 = 16
- 16: 1 + 6 = 7
The digital root is 7. Reversing its digits gives 088; 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, 880/100 simplifies to 44/5 by dividing both terms by their greatest common divisor, 20. Its decimal value is 8.8. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 880 and 12 is 4. Their least common multiple is 2640. The identity GCD × LCM = 880 × 12 = 10560 checks both results.
Work through GCF and LCMQuestions about 880
What are the factors of 880?
The positive factors are 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440, 880. There are 20 factors, including 1 and 880.
Is 880 a prime number?
No. 880 is composite: 2^4 × 5 × 11 = 880.
How do you write 880 in Roman numerals?
880 is DCCCLXXX in standard subtractive Roman numeral notation.
What is the binary representation of 880?
880 in decimal is 1101110000 in base 2. Adding its active place values gives 512 + 256 + 64 + 32 + 16 = 880.
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 880
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 880 add to 16. 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.