The number 997
997 is the 168th prime number. Its only divisors are 1 and 997.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 997: the 168th prime number.
- 2
997 is prime, so its only factors are 1 and 997. It is the 168th prime; the next prime is 1009 and the one before is 991.
- 3
The divisors add up to 998; without 997 itself that is 1, so 997 is deficient (1 is less than 997). Euler's totient φ(997) = 996 numbers up to 997 share no factor with it.
- 4
The digits of 997 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
997 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 998 |
| Euler totient φ(n) | 996 |
| Square | 994009 |
| Cube | 991026973 |
| Square root | 31.575307 |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 49 |
| Scientific notation | 9.97 × |
997 in other forms
| Form | Value |
|---|---|
| In words | nine hundred and ninety-seven |
| Roman numerals | CMXCVII |
| Binary (base 2) | 1111100101 |
| Octal (base 8) | 1745 |
| Hexadecimal (base 16) | 3E5 |
| Base 3 | 1100221 |
| As time | 997 seconds = 16 min 37 s |
Is 997 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 2) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | 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 997 a prime number?
Yes. 997 is divisible only by 1 and itself.
What are the factors of 997?
1, 997.
What is 997 in binary?
1111100101 (hexadecimal 3E5, octal 1745).
What is the square root of 997?
About 31.5753.
What is 997 in Roman numerals?
CMXCVII.
Is 997 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 997?
997 is the 168th prime number.