Number dictionary · Exact arithmetic
888: factors and number facts
eight hundred eighty-eight is an even number and is composite. Its 16 positive divisors form 8 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- eight hundred eighty-eight
- Roman numeral
- DCCCLXXXVIII
- Prime factorization
- 2^3 × 3 × 37
- Digital root
- 6
All factors of 888
A positive factor divides 888 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 6, 8, 12, 24, 37, 74, 111, 148, 222, 296, 444, 888
Factor pairs
- 1 × 888 = 888
- 2 × 444 = 888
- 3 × 296 = 888
- 4 × 222 = 888
- 6 × 148 = 888
- 8 × 111 = 888
- 12 × 74 = 888
- 24 × 37 = 888
Each pair describes an arrangement of 888 items into equal rows. The pairs have different row and column counts; 888 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 16
- Sum of all divisors
- 2280
- Sum excluding 888
- 1392
- Classification
- abundant
888 is abundant because its proper divisors add to 1392, which is greater than 888.
Prime factorization of 888
888 = 2^3 × 3 × 37
Repeated division, step by step
- 888 ÷ 2 = 444
- 444 ÷ 2 = 222
- 222 ÷ 2 = 111
- 111 ÷ 3 = 37
- 37 ÷ 37 = 1
Multiply the prime divisors in these steps to reconstruct 888. An exponent records how many times the same prime occurs. The divisor-count calculation is (3 + 1) × (1 + 1) × (1 + 1) = 16.
The preceding prime is 887. The next larger prime is 907. The factor list above explains why 888 is composite.
Learn the factorization method888 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | eight hundred eighty-eight |
| Roman numeral | DCCCLXXXVIII |
| Binary (base 2) | 1101111000 |
| Octal (base 8) | 1570 |
| Decimal (base 10) | 888 |
| Hexadecimal (base 16) | 378 |
Check the binary conversion
Read 1101111000 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 + 8 = 888
Check the hexadecimal conversion
3 × 16^2 + 7 × 16^1 + 8 × 16^0 = 888
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 888
- 888 squared
- 888 × 888 = 788,544
- 888 cubed
- 888 × 888 × 888 = 700,227,072
- Square root
- ≈ 29.799329
- Simplified radical
- 2√222
888 lies between 841 (29²) and 900 (30²), so it is not a perfect square. It is not a perfect cube.
888 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 888.
Distinguish a square from a square rootMultiplication table for 888
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 | 444 | 0 | Yes |
| 3 | 296 | 0 | Yes |
| 4 | 222 | 0 | Yes |
| 5 | 177 | 3 | No |
| 6 | 148 | 0 | Yes |
| 7 | 126 | 6 | No |
| 8 | 111 | 0 | Yes |
| 9 | 98 | 6 | No |
| 10 | 88 | 8 | No |
| 11 | 80 | 8 | No |
| 12 | 74 | 0 | Yes |
For example, 888 = 7 × 126 + 6. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 888
888 contains 3 decimal digits. Its digit sum is 8 + 8 + 8 = 24.
- 888: 8 + 8 + 8 = 24
- 24: 2 + 4 = 6
The digital root is 6. 888 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, 888/100 simplifies to 222/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 8.88. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 888 and 12 is 12. Their least common multiple is 888. The identity GCD × LCM = 888 × 12 = 10656 checks both results.
Work through GCF and LCMQuestions about 888
What are the factors of 888?
The positive factors are 1, 2, 3, 4, 6, 8, 12, 24, 37, 74, 111, 148, 222, 296, 444, 888. There are 16 factors, including 1 and 888.
Is 888 a prime number?
No. 888 is composite: 2^3 × 3 × 37 = 888.
How do you write 888 in Roman numerals?
888 is DCCCLXXXVIII in standard subtractive Roman numeral notation.
What is the binary representation of 888?
888 in decimal is 1101111000 in base 2. Adding its active place values gives 512 + 256 + 64 + 32 + 16 + 8 = 888.
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 888
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 888 add to 24. 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.