The number 971
971 is the 164th prime number. Its only divisors are 1 and 971.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 971: the 164th prime number.
- 2
971 is prime, so its only factors are 1 and 971. It is the 164th prime; the next prime is 977 and the one before is 967.
- 3
The divisors add up to 972; without 971 itself that is 1, so 971 is deficient (1 is less than 971). Euler's totient φ(971) = 970 numbers up to 971 share no factor with it.
- 4
The digits of 971 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
971 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 972 |
| Euler totient φ(n) | 970 |
| Square | 942841 |
| Cube | 915498611 |
| Square root | 31.160873 |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 36 |
| Scientific notation | 9.71 × |
971 in other forms
| Form | Value |
|---|---|
| In words | nine hundred and seventy-one |
| Roman numerals | CMLXXI |
| Binary (base 2) | 1111001011 |
| Octal (base 8) | 1713 |
| Hexadecimal (base 16) | 3CB |
| Base 3 | 1022222 |
| As time | 971 seconds = 16 min 11 s |
Is 971 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 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 8) | 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 3) | 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 971 a prime number?
Yes. 971 is divisible only by 1 and itself.
What are the factors of 971?
1, 971.
What is 971 in binary?
1111001011 (hexadecimal 3CB, octal 1713).
What is the square root of 971?
About 31.1609.
What is 971 in Roman numerals?
CMLXXI.
Is 971 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 971?
971 is the 164th prime number.