Number dictionary · Exact arithmetic
988: factors and number facts
nine hundred eighty-eight is an even number and is composite. Its 12 positive divisors form 6 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- nine hundred eighty-eight
- Roman numeral
- CMLXXXVIII
- Prime factorization
- 2^2 × 13 × 19
- Digital root
- 7
All factors of 988
A positive factor divides 988 with no remainder. In ascending order, the complete list is:
1, 2, 4, 13, 19, 26, 38, 52, 76, 247, 494, 988
Factor pairs
- 1 × 988 = 988
- 2 × 494 = 988
- 4 × 247 = 988
- 13 × 76 = 988
- 19 × 52 = 988
- 26 × 38 = 988
Each pair describes an arrangement of 988 items into equal rows. The pairs have different row and column counts; 988 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 12
- Sum of all divisors
- 1960
- Sum excluding 988
- 972
- Classification
- deficient
988 is deficient because its proper divisors add to 972, which is less than 988.
Prime factorization of 988
988 = 2^2 × 13 × 19
Repeated division, step by step
- 988 ÷ 2 = 494
- 494 ÷ 2 = 247
- 247 ÷ 13 = 19
- 19 ÷ 19 = 1
Multiply the prime divisors in these steps to reconstruct 988. An exponent records how many times the same prime occurs. The divisor-count calculation is (2 + 1) × (1 + 1) × (1 + 1) = 12.
The preceding prime is 983. The next larger prime is 991. The factor list above explains why 988 is composite.
Learn the factorization method988 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | nine hundred eighty-eight |
| Roman numeral | CMLXXXVIII |
| Binary (base 2) | 1111011100 |
| Octal (base 8) | 1734 |
| Decimal (base 10) | 988 |
| Hexadecimal (base 16) | 3DC |
Check the binary conversion
Read 1111011100 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 + 16 + 8 + 4 = 988
Check the hexadecimal conversion
3 × 16^2 + 13 × 16^1 + 12 × 16^0 = 988
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 988
- 988 squared
- 988 × 988 = 976,144
- 988 cubed
- 988 × 988 × 988 = 964,430,272
- Square root
- ≈ 31.432467
- Simplified radical
- 2√247
988 lies between 961 (31²) and 1024 (32²), so it is not a perfect square. It is not a perfect cube.
988 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 988.
Distinguish a square from a square rootMultiplication table for 988
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 | 494 | 0 | Yes |
| 3 | 329 | 1 | No |
| 4 | 247 | 0 | Yes |
| 5 | 197 | 3 | No |
| 6 | 164 | 4 | No |
| 7 | 141 | 1 | No |
| 8 | 123 | 4 | No |
| 9 | 109 | 7 | No |
| 10 | 98 | 8 | No |
| 11 | 89 | 9 | No |
| 12 | 82 | 4 | No |
For example, 988 = 7 × 141 + 1. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 988
988 contains 3 decimal digits. Its digit sum is 9 + 8 + 8 = 25.
- 988: 9 + 8 + 8 = 25
- 25: 2 + 5 = 7
The digital root is 7. Reversing its digits gives 889; 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, 988/100 simplifies to 247/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 9.88. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 988 and 12 is 4. Their least common multiple is 2964. The identity GCD × LCM = 988 × 12 = 11856 checks both results.
Work through GCF and LCMQuestions about 988
What are the factors of 988?
The positive factors are 1, 2, 4, 13, 19, 26, 38, 52, 76, 247, 494, 988. There are 12 factors, including 1 and 988.
Is 988 a prime number?
No. 988 is composite: 2^2 × 13 × 19 = 988.
How do you write 988 in Roman numerals?
988 is CMLXXXVIII in standard subtractive Roman numeral notation.
What is the binary representation of 988?
988 in decimal is 1111011100 in base 2. Adding its active place values gives 512 + 256 + 128 + 64 + 16 + 8 + 4 = 988.
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 988
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 988 add to 25. 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.