The number 1931
1931 is a twin prime (1931 and 1933 are both prime) and the 294th prime number. Its only divisors are 1 and 1931.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1931: a twin prime (1931 and 1933 are both prime); the 294th prime number.
- 2
1931 is prime, so its only factors are 1 and 1931. It is the 294th prime; the next prime is 1933 and the one before is 1913.
- 3
The divisors add up to 1932; without 1931 itself that is 1, so 1931 is deficient (1 is less than 1931). Euler's totient φ(1931) = 1930 numbers up to 1931 share no factor with it.
- 4
The digits of 1931 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 143 steps to reach 1.
1931 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1932 |
| Euler totient φ(n) | 1930 |
| Square | 3728761 |
| Cube | 7200237491 |
| Square root | 43.943145 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 143 |
| Scientific notation | 1.931 × |
1931 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and thirty-one |
| Roman numerals | MCMXXXI |
| Binary (base 2) | 11110001011 |
| Octal (base 8) | 3613 |
| Hexadecimal (base 16) | 78B |
| Base 3 | 2122112 |
| As time | 1931 seconds = 32 min 11 s |
Is 1931 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 2) | 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 5) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1931 a prime number?
Yes. 1931 is divisible only by 1 and itself.
What are the factors of 1931?
1, 1931.
What is 1931 in binary?
11110001011 (hexadecimal 78B, octal 3613).
What is the square root of 1931?
About 43.9431.
What is 1931 in Roman numerals?
MCMXXXI.
Is 1931 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 1931?
1931 is a twin prime (1931 and 1933 are both prime); the 294th prime number.