The number 8101
8101 is the 1019th prime number. Its only divisors are 1 and 8101.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8101: the 1019th prime number.
- 2
8101 is prime, so its only factors are 1 and 8101. It is the 1019th prime; the next prime is 8111 and the one before is 8093.
- 3
The divisors add up to 8102; without 8101 itself that is 1, so 8101 is deficient (1 is less than 8101). Euler's totient φ(8101) = 8100 numbers up to 8101 share no factor with it.
- 4
The digits of 8101 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 158 steps to reach 1.
8101 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 8102 |
| Euler totient φ(n) | 8100 |
| Square | 65626201 |
| Cube | 531637854301 |
| Square root | 90.005555 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 158 |
| Scientific notation | 8.101 × |
8101 in other forms
| Form | Value |
|---|---|
| In words | eight thousand one hundred and one |
| Binary (base 2) | 1111110100101 |
| Octal (base 8) | 17645 |
| Hexadecimal (base 16) | 1FA5 |
| Base 3 | 102010001 |
| As time | 8101 seconds = 2 h 15 min 1 s |
Is 8101 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 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 5) | 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 5) | 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 8101 a prime number?
Yes. 8101 is divisible only by 1 and itself.
What are the factors of 8101?
1, 8101.
What is 8101 in binary?
1111110100101 (hexadecimal 1FA5, octal 17645).
What is the square root of 8101?
About 90.0056.
Is 8101 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 8101?
8101 is the 1019th prime number.