The number 108
108 is a composite number with 12 divisors. Its prime factorisation is × . Divisors (12): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 108: a Harshad number: divisible by its digit sum 9.
- 2
108 is composite. Its prime factorisation is
- 3
The divisors add up to 280; without 108 itself that is 172, so 108 is abundant (172 is more than 108). Euler's totient φ(108) = 36 numbers up to 108 share no factor with it.
- 4
The digits of 108 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 113 steps to reach 1.
LaTeX source of the formulas on this page
\[ 108 = 2^{2} \times 3^{3} \]108 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 280 |
| Euler totient φ(n) | 36 |
| Square | 11664 |
| Cube | 1259712 |
| Square root | 10.392305 (= 6√3) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 113 |
| Scientific notation | 1.08 × |
108 in other forms
| Form | Value |
|---|---|
| In words | one hundred and eight |
| Roman numerals | CVIII |
| Binary (base 2) | 1101100 |
| Octal (base 8) | 154 |
| Hexadecimal (base 16) | 6C |
| Base 3 | 11000 |
| As time | 108 seconds = 1 min 48 s |
Is 108 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (108 ÷ 2 = 54) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (108 ÷ 3 = 36) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (108 ÷ 4 = 27) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (108 ÷ 6 = 18) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (108 ÷ 9 = 12) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (108 ÷ 12 = 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 108 a prime number?
No. 108 = × , so it is divisible by 2.
What are the factors of 108?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.
What is 108 in binary?
1101100 (hexadecimal 6C, octal 154).
What is the square root of 108?
About 10.3923, exactly 6√3.
What is 108 in Roman numerals?
CVIII.
Is 108 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 108?
108 is a Harshad number: divisible by its digit sum 9.