Number dictionary · Exact arithmetic
998: factors and number facts
nine hundred ninety-eight is an even number and is composite. Its 4 positive divisors form 2 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- nine hundred ninety-eight
- Roman numeral
- CMXCVIII
- Prime factorization
- 2 × 499
- Digital root
- 8
All factors of 998
A positive factor divides 998 with no remainder. In ascending order, the complete list is:
1, 2, 499, 998
Factor pairs
- 1 × 998 = 998
- 2 × 499 = 998
Each pair describes an arrangement of 998 items into equal rows. The pairs have different row and column counts; 998 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 4
- Sum of all divisors
- 1500
- Sum excluding 998
- 502
- Classification
- deficient
998 is deficient because its proper divisors add to 502, which is less than 998.
Prime factorization of 998
998 = 2 × 499
Repeated division, step by step
- 998 ÷ 2 = 499
- 499 ÷ 499 = 1
Multiply the prime divisors in these steps to reconstruct 998. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) = 4.
The preceding prime is 997. The next larger prime is 1009. The factor list above explains why 998 is composite.
Learn the factorization method998 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | nine hundred ninety-eight |
| Roman numeral | CMXCVIII |
| Binary (base 2) | 1111100110 |
| Octal (base 8) | 1746 |
| Decimal (base 10) | 998 |
| Hexadecimal (base 16) | 3E6 |
Check the binary conversion
Read 1111100110 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 + 4 + 2 = 998
Check the hexadecimal conversion
3 × 16^2 + 14 × 16^1 + 6 × 16^0 = 998
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 998
- 998 squared
- 998 × 998 = 996,004
- 998 cubed
- 998 × 998 × 998 = 994,011,992
- Square root
- ≈ 31.591138
- Simplified radical
- √998
998 lies between 961 (31²) and 1024 (32²), so it is not a perfect square. It is not a perfect cube.
998 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 998.
Distinguish a square from a square rootMultiplication table for 998
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 | 499 | 0 | Yes |
| 3 | 332 | 2 | No |
| 4 | 249 | 2 | No |
| 5 | 199 | 3 | No |
| 6 | 166 | 2 | No |
| 7 | 142 | 4 | No |
| 8 | 124 | 6 | No |
| 9 | 110 | 8 | No |
| 10 | 99 | 8 | No |
| 11 | 90 | 8 | No |
| 12 | 83 | 2 | No |
For example, 998 = 7 × 142 + 4. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 998
998 contains 3 decimal digits. Its digit sum is 9 + 9 + 8 = 26.
- 998: 9 + 9 + 8 = 26
- 26: 2 + 6 = 8
The digital root is 8. Reversing its digits gives 899; 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, 998/100 simplifies to 499/50 by dividing both terms by their greatest common divisor, 2. Its decimal value is 9.98. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 998 and 12 is 2. Their least common multiple is 5988. The identity GCD × LCM = 998 × 12 = 11976 checks both results.
Work through GCF and LCMQuestions about 998
What are the factors of 998?
The positive factors are 1, 2, 499, 998. There are 4 factors, including 1 and 998.
Is 998 a prime number?
No. 998 is composite: 2 × 499 = 998.
How do you write 998 in Roman numerals?
998 is CMXCVIII in standard subtractive Roman numeral notation.
What is the binary representation of 998?
998 in decimal is 1111100110 in base 2. Adding its active place values gives 512 + 256 + 128 + 64 + 32 + 4 + 2 = 998.
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 998
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 998 add to 26. 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.