The number 1997
1997 is a twin prime (1997 and 1999 are both prime) and the 302nd prime number. Its only divisors are 1 and 1997.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1997: a twin prime (1997 and 1999 are both prime); the 302nd prime number.
- 2
1997 is prime, so its only factors are 1 and 1997. It is the 302nd prime; the next prime is 1999 and the one before is 1993.
- 3
The divisors add up to 1998; without 1997 itself that is 1, so 1997 is deficient (1 is less than 1997). Euler's totient φ(1997) = 1996 numbers up to 1997 share no factor with it.
- 4
The digits of 1997 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
1997 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1998 |
| Euler totient φ(n) | 1996 |
| Square | 3988009 |
| Cube | 7964053973 |
| Square root | 44.687806 |
| Digit sum / digital root | 26 / 8 |
| Collatz steps to 1 | 50 |
| Scientific notation | 1.997 × |
1997 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and ninety-seven |
| Roman numerals | MCMXCVII |
| Binary (base 2) | 11111001101 |
| Octal (base 8) | 3715 |
| Hexadecimal (base 16) | 7CD |
| Base 3 | 2201222 |
| As time | 1997 seconds = 33 min 17 s |
Is 1997 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 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 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 8) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1997 a prime number?
Yes. 1997 is divisible only by 1 and itself.
What are the factors of 1997?
1, 1997.
What is 1997 in binary?
11111001101 (hexadecimal 7CD, octal 3715).
What is the square root of 1997?
About 44.6878.
What is 1997 in Roman numerals?
MCMXCVII.
Is 1997 divisible by 3?
No. Its digits add up to 26, which is not a multiple of 3.
What is special about the number 1997?
1997 is a twin prime (1997 and 1999 are both prime); the 302nd prime number.