The number 243
243 is a perfect power (). Its prime factorisation is . Divisors (6): 1, 3, 9, 27, 81, 243.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 243: a perfect power (); a Harshad number: divisible by its digit sum 9.
- 2
243 is composite. Its prime factorisation is
- 3
The divisors add up to 364; without 243 itself that is 121, so 243 is deficient (121 is less than 243). Euler's totient φ(243) = 162 numbers up to 243 share no factor with it.
- 4
The digits of 243 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 96 steps to reach 1.
LaTeX source of the formulas on this page
\[ 243 = 3^{5} \]243 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 364 |
| Euler totient φ(n) | 162 |
| Square | 59049 |
| Cube | 14348907 |
| Square root | 15.588457 (= 9√3) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 96 |
| Scientific notation | 2.43 × |
| Perfect power |
243 in other forms
| Form | Value |
|---|---|
| In words | two hundred and forty-three |
| Roman numerals | CCXLIII |
| Binary (base 2) | 11110011 |
| Octal (base 8) | 363 |
| Hexadecimal (base 16) | F3 |
| Base 3 | 100000 |
| As time | 243 seconds = 4 min 3 s |
Is 243 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (243 ÷ 3 = 81) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | 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 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (243 ÷ 9 = 27) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 243 a prime number?
No. 243 = , so it is divisible by 3.
What are the factors of 243?
1, 3, 9, 27, 81, 243.
What is 243 in binary?
11110011 (hexadecimal F3, octal 363).
What is the square root of 243?
About 15.5885, exactly 9√3.
What is 243 in Roman numerals?
CCXLIII.
Is 243 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 243?
243 is a perfect power (); a Harshad number: divisible by its digit sum 9.