The number 198
198 is a composite number with 12 divisors. Its prime factorisation is 2 × × 11. Divisors (12): 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 198: a Harshad number: divisible by its digit sum 18.
- 2
198 is composite. Its prime factorisation is
- 3
The divisors add up to 468; without 198 itself that is 270, so 198 is abundant (270 is more than 198). Euler's totient φ(198) = 60 numbers up to 198 share no factor with it.
- 4
The digits of 198 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 26 steps to reach 1.
LaTeX source of the formulas on this page
\[ 198 = 2 \times 3^{2} \times 11 \]198 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 468 |
| Euler totient φ(n) | 60 |
| Square | 39204 |
| Cube | 7762392 |
| Square root | 14.071247 (= 3√22) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 26 |
| Scientific notation | 1.98 × |
198 in other forms
| Form | Value |
|---|---|
| In words | one hundred and ninety-eight |
| Roman numerals | CXCVIII |
| Binary (base 2) | 11000110 |
| Octal (base 8) | 306 |
| Hexadecimal (base 16) | C6 |
| Base 3 | 21100 |
| As time | 198 seconds = 3 min 18 s |
Is 198 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (198 ÷ 2 = 99) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (198 ÷ 3 = 66) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | 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 (198 ÷ 6 = 33) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (198 ÷ 9 = 22) | 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 | Yes (198 ÷ 11 = 18) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 198 a prime number?
No. 198 = 2 × × 11, so it is divisible by 2.
What are the factors of 198?
1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198.
What is 198 in binary?
11000110 (hexadecimal C6, octal 306).
What is the square root of 198?
About 14.0712, exactly 3√22.
What is 198 in Roman numerals?
CXCVIII.
Is 198 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 198?
198 is a Harshad number: divisible by its digit sum 18.