The number 231
231 is a triangular number: 1 + 2 + … + 21 = 231 and a binary palindrome (11100111). Its prime factorisation is 3 × 7 × 11. Divisors (8): 1, 3, 7, 11, 21, 33, 77, 231.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 231: a triangular number: 1 + 2 + … + 21 = 231; a binary palindrome (11100111).
- 2
231 is composite. Its prime factorisation is
- 3
The divisors add up to 384; without 231 itself that is 153, so 231 is deficient (153 is less than 231). Euler's totient φ(231) = 120 numbers up to 231 share no factor with it.
- 4
The digits of 231 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 127 steps to reach 1.
LaTeX source of the formulas on this page
\[ 231 = 3 \times 7 \times 11 \]
231 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 384 |
| Euler totient φ(n) | 120 |
| Square | 53361 |
| Cube | 12326391 |
| Square root | 15.198684 |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 127 |
| Scientific notation | 2.31 × |
231 in other forms
| Form | Value |
|---|---|
| In words | two hundred and thirty-one |
| Roman numerals | CCXXXI |
| Binary (base 2) | 11100111 |
| Octal (base 8) | 347 |
| Hexadecimal (base 16) | E7 |
| Base 3 | 22120 |
| As time | 231 seconds = 3 min 51 s |
Is 231 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 (231 ÷ 3 = 77) | 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 1) | 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 | Yes (231 ÷ 7 = 33) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (231 ÷ 11 = 21) | 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 231 a prime number?
No. 231 = 3 × 7 × 11, so it is divisible by 3.
What are the factors of 231?
1, 3, 7, 11, 21, 33, 77, 231.
What is 231 in binary?
11100111 (hexadecimal E7, octal 347).
What is the square root of 231?
About 15.1987.
What is 231 in Roman numerals?
CCXXXI.
Is 231 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 231?
231 is a triangular number: 1 + 2 + … + 21 = 231; a binary palindrome (11100111).