The number 17971
17971 is a palindromic prime: it reads the same backwards and is prime, the 2060th prime number and a palindrome: it reads 17971 backwards too. Its only divisors are 1 and 17971.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 17971: a palindromic prime: it reads the same backwards and is prime; the 2060th prime number; a palindrome: it reads 17971 backwards too.
- 2
17971 is prime, so its only factors are 1 and 17971. It is the 2060th prime; the next prime is 17977 and the one before is 17959.
- 3
The divisors add up to 17972; without 17971 itself that is 1, so 17971 is deficient (1 is less than 17971). Euler's totient φ(17971) = 17970 numbers up to 17971 share no factor with it.
- 4
The digits of 17971 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 185 steps to reach 1.
17971 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 17972 |
| Euler totient φ(n) | 17970 |
| Square | 322956841 |
| Cube | 5803857389611 |
| Square root | 134.055958 |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 185 |
| Scientific notation | 1.7971 × |
17971 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand nine hundred and seventy-one |
| Binary (base 2) | 100011000110011 |
| Octal (base 8) | 43063 |
| Hexadecimal (base 16) | 4633 |
| Base 3 | 220122121 |
| As time | 17971 seconds = 4 h 59 min 31 s |
Is 17971 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 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 3) | 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 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | 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 17971 a prime number?
Yes. 17971 is divisible only by 1 and itself.
What are the factors of 17971?
1, 17971.
What is 17971 in binary?
100011000110011 (hexadecimal 4633, octal 43063).
What is the square root of 17971?
About 134.0560.
Is 17971 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 17971?
17971 is a palindromic prime: it reads the same backwards and is prime; the 2060th prime number; a palindrome: it reads 17971 backwards too.