The number 9931
9931 is a twin prime (9929 and 9931 are both prime) and the 1225th prime number. Its only divisors are 1 and 9931.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9931: a twin prime (9929 and 9931 are both prime); the 1225th prime number.
- 2
9931 is prime, so its only factors are 1 and 9931. It is the 1225th prime; the next prime is 9941 and the one before is 9929.
- 3
The divisors add up to 9932; without 9931 itself that is 1, so 9931 is deficient (1 is less than 9931). Euler's totient φ(9931) = 9930 numbers up to 9931 share no factor with it.
- 4
The digits of 9931 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 117 steps to reach 1.
9931 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 9932 |
| Euler totient φ(n) | 9930 |
| Square | 98624761 |
| Cube | 979442501491 |
| Square root | 99.654403 |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 117 |
| Scientific notation | 9.931 × |
9931 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and thirty-one |
| Binary (base 2) | 10011011001011 |
| Octal (base 8) | 23313 |
| Hexadecimal (base 16) | 26CB |
| Base 3 | 111121211 |
| As time | 9931 seconds = 2 h 45 min 31 s |
Is 9931 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 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 | 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 9931 a prime number?
Yes. 9931 is divisible only by 1 and itself.
What are the factors of 9931?
1, 9931.
What is 9931 in binary?
10011011001011 (hexadecimal 26CB, octal 23313).
What is the square root of 9931?
About 99.6544.
Is 9931 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 9931?
9931 is a twin prime (9929 and 9931 are both prime); the 1225th prime number.