The number 192
192 is a composite number with 14 divisors. Its prime factorisation is × 3. Divisors (14): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 192: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.
- 2
192 is composite. Its prime factorisation is
- 3
The divisors add up to 508; without 192 itself that is 316, so 192 is abundant (316 is more than 192). Euler's totient φ(192) = 64 numbers up to 192 share no factor with it.
- 4
The digits of 192 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 13 steps to reach 1.
LaTeX source of the formulas on this page
\[ 192 = 2^{6} \times 3 \]192 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 14 |
| Sum of divisors | 508 |
| Euler totient φ(n) | 64 |
| Square | 36864 |
| Cube | 7077888 |
| Square root | 13.856406 (= 8√3) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 13 |
| Scientific notation | 1.92 × |
192 in other forms
| Form | Value |
|---|---|
| In words | one hundred and ninety-two |
| Roman numerals | CXCII |
| Binary (base 2) | 11000000 |
| Octal (base 8) | 300 |
| Hexadecimal (base 16) | C0 |
| Base 3 | 21010 |
| As time | 192 seconds = 3 min 12 s |
Is 192 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (192 ÷ 2 = 96) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (192 ÷ 3 = 64) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (192 ÷ 4 = 48) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (192 ÷ 6 = 32) | 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 | Yes (192 ÷ 8 = 24) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (192 ÷ 12 = 16) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 192 a prime number?
No. 192 = × 3, so it is divisible by 2.
What are the factors of 192?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192.
What is 192 in binary?
11000000 (hexadecimal C0, octal 300).
What is the square root of 192?
About 13.8564, exactly 8√3.
What is 192 in Roman numerals?
CXCII.
Is 192 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 192?
192 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.