The number 991
991 is the 167th prime number. Its only divisors are 1 and 991.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 991: the 167th prime number.
- 2
991 is prime, so its only factors are 1 and 991. It is the 167th prime; the next prime is 997 and the one before is 983.
- 3
The divisors add up to 992; without 991 itself that is 1, so 991 is deficient (1 is less than 991). Euler's totient φ(991) = 990 numbers up to 991 share no factor with it.
- 4
The digits of 991 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 98 steps to reach 1.
991 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 992 |
| Euler totient φ(n) | 990 |
| Square | 982081 |
| Cube | 973242271 |
| Square root | 31.480152 |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 98 |
| Scientific notation | 9.91 × |
991 in other forms
| Form | Value |
|---|---|
| In words | nine hundred and ninety-one |
| Roman numerals | CMXCI |
| Binary (base 2) | 1111011111 |
| Octal (base 8) | 1737 |
| Hexadecimal (base 16) | 3DF |
| Base 3 | 1100201 |
| As time | 991 seconds = 16 min 31 s |
Is 991 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 4) | 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 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 1) | 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 991 a prime number?
Yes. 991 is divisible only by 1 and itself.
What are the factors of 991?
1, 991.
What is 991 in binary?
1111011111 (hexadecimal 3DF, octal 1737).
What is the square root of 991?
About 31.4802.
What is 991 in Roman numerals?
CMXCI.
Is 991 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 991?
991 is the 167th prime number.