Number dictionary · Exact arithmetic
108: factors and number facts
one hundred 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
- one hundred eight
- Roman numeral
- CVIII
- Prime factorization
- 2^2 × 3^3
- Digital root
- 9
All factors of 108
A positive factor divides 108 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Factor pairs
- 1 × 108 = 108
- 2 × 54 = 108
- 3 × 36 = 108
- 4 × 27 = 108
- 6 × 18 = 108
- 9 × 12 = 108
Each pair describes an arrangement of 108 items into equal rows. The pairs have different row and column counts; 108 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 12
- Sum of all divisors
- 280
- Sum excluding 108
- 172
- Classification
- abundant
108 is abundant because its proper divisors add to 172, which is greater than 108.
Prime factorization of 108
108 = 2^2 × 3^3
Repeated division, step by step
- 108 ÷ 2 = 54
- 54 ÷ 2 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1
Multiply the prime divisors in these steps to reconstruct 108. An exponent records how many times the same prime occurs. The divisor-count calculation is (2 + 1) × (3 + 1) = 12.
The preceding prime is 107. The next larger prime is 109. The factor list above explains why 108 is composite.
Learn the factorization method108 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one hundred eight |
| Roman numeral | CVIII |
| Binary (base 2) | 1101100 |
| Octal (base 8) | 154 |
| Decimal (base 10) | 108 |
| Hexadecimal (base 16) | 6C |
Check the binary conversion
Read 1101100 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
64 + 32 + 8 + 4 = 108
Check the hexadecimal conversion
6 × 16^1 + 12 × 16^0 = 108
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 108
- 108 squared
- 108 × 108 = 11,664
- 108 cubed
- 108 × 108 × 108 = 1,259,712
- Square root
- ≈ 10.392305
- Simplified radical
- 6√3
108 lies between 100 (10²) and 121 (11²), so it is not a perfect square. It is not a perfect cube.
108 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 108.
Distinguish a square from a square rootMultiplication table for 108
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 | 54 | 0 | Yes |
| 3 | 36 | 0 | Yes |
| 4 | 27 | 0 | Yes |
| 5 | 21 | 3 | No |
| 6 | 18 | 0 | Yes |
| 7 | 15 | 3 | No |
| 8 | 13 | 4 | No |
| 9 | 12 | 0 | Yes |
| 10 | 10 | 8 | No |
| 11 | 9 | 9 | No |
| 12 | 9 | 0 | Yes |
For example, 108 = 7 × 15 + 3. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 108
108 contains 3 decimal digits. Its digit sum is 1 + 0 + 8 = 9.
- 108: 1 + 0 + 8 = 9
The digital root is 9. Reversing its digits gives 801; 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, 108/100 simplifies to 27/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 1.08. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 108 and 12 is 12. Their least common multiple is 108. The identity GCD × LCM = 108 × 12 = 1296 checks both results.
Work through GCF and LCMQuestions about 108
What are the factors of 108?
The positive factors are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. There are 12 factors, including 1 and 108.
Is 108 a prime number?
No. 108 is composite: 2^2 × 3^3 = 108.
How do you write 108 in Roman numerals?
108 is CVIII in standard subtractive Roman numeral notation.
What is the binary representation of 108?
108 in decimal is 1101100 in base 2. Adding its active place values gives 64 + 32 + 8 + 4 = 108.
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 108
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 108 add to 9. 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.