The number 31
31 is a Mersenne prime ( − 1), a twin prime (29 and 31 are both prime) and the 11th prime number. Its only divisors are 1 and 31.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 31: a Mersenne prime ( − 1); a twin prime (29 and 31 are both prime); the 11th prime number; a binary palindrome (11111); a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
31 is prime, so its only factors are 1 and 31. It is the 11th prime; the next prime is 37 and the one before is 29.
- 3
The divisors add up to 32; without 31 itself that is 1, so 31 is deficient (1 is less than 31). Euler's totient φ(31) = 30 numbers up to 31 share no factor with it.
- 4
The digits of 31 add up to 4, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 106 steps to reach 1.
31 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 32 |
| Euler totient φ(n) | 30 |
| Square | 961 |
| Cube | 29791 |
| Square root | 5.567764 |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 106 |
| Scientific notation | 3.1 × |
31 in other forms
| Form | Value |
|---|---|
| In words | thirty-one |
| Roman numerals | XXXI |
| Binary (base 2) | 11111 |
| Octal (base 8) | 37 |
| Hexadecimal (base 16) | 1F |
| Base 3 | 1011 |
| As time | 31 seconds |
Is 31 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 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 1) | 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 | No (remainder 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31 a prime number?
Yes. 31 is divisible only by 1 and itself.
What are the factors of 31?
1, 31.
What is 31 in binary?
11111 (hexadecimal 1F, octal 37).
What is the square root of 31?
About 5.5678.
What is 31 in Roman numerals?
XXXI.
Is 31 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 31?
31 is a Mersenne prime ( − 1); a twin prime (29 and 31 are both prime); the 11th prime number; a binary palindrome (11111); a happy number: repeatedly adding the squares of its digits reaches 1.