The number 181
181 is a palindromic prime: it reads the same backwards and is prime, a twin prime (179 and 181 are both prime) and the 42nd prime number. Its only divisors are 1 and 181.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 181: a palindromic prime: it reads the same backwards and is prime; a twin prime (179 and 181 are both prime); the 42nd prime number; a palindrome: it reads 181 backwards too.
- 2
181 is prime, so its only factors are 1 and 181. It is the 42nd prime; the next prime is 191 and the one before is 179.
- 3
The divisors add up to 182; without 181 itself that is 1, so 181 is deficient (1 is less than 181). Euler's totient φ(181) = 180 numbers up to 181 share no factor with it.
- 4
The digits of 181 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 18 steps to reach 1.
181 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 182 |
| Euler totient φ(n) | 180 |
| Square | 32761 |
| Cube | 5929741 |
| Square root | 13.453624 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 18 |
| Scientific notation | 1.81 × |
181 in other forms
| Form | Value |
|---|---|
| In words | one hundred and eighty-one |
| Roman numerals | CLXXXI |
| Binary (base 2) | 10110101 |
| Octal (base 8) | 265 |
| Hexadecimal (base 16) | B5 |
| Base 3 | 20201 |
| As time | 181 seconds = 3 min 1 s |
Is 181 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 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 181 a prime number?
Yes. 181 is divisible only by 1 and itself.
What are the factors of 181?
1, 181.
What is 181 in binary?
10110101 (hexadecimal B5, octal 265).
What is the square root of 181?
About 13.4536.
What is 181 in Roman numerals?
CLXXXI.
Is 181 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 181?
181 is a palindromic prime: it reads the same backwards and is prime; a twin prime (179 and 181 are both prime); the 42nd prime number; a palindrome: it reads 181 backwards too.