The number 10067
10067 is a twin prime (10067 and 10069 are both prime) and the 1235th prime number. Its only divisors are 1 and 10067.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10067: a twin prime (10067 and 10069 are both prime); the 1235th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
10067 is prime, so its only factors are 1 and 10067. It is the 1235th prime; the next prime is 10069 and the one before is 10061.
- 3
The divisors add up to 10068; without 10067 itself that is 1, so 10067 is deficient (1 is less than 10067). Euler's totient φ(10067) = 10066 numbers up to 10067 share no factor with it.
- 4
The digits of 10067 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 91 steps to reach 1.
10067 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 10068 |
| Euler totient φ(n) | 10066 |
| Square | 101344489 |
| Cube | 1020234970763 |
| Square root | 100.334441 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 91 |
| Scientific notation | 1.0067 × |
10067 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and sixty-seven |
| Binary (base 2) | 10011101010011 |
| Octal (base 8) | 23523 |
| Hexadecimal (base 16) | 2753 |
| Base 3 | 111210212 |
| As time | 10067 seconds = 2 h 47 min 47 s |
Is 10067 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 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 1) | 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 5) | 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 2) | 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 10067 a prime number?
Yes. 10067 is divisible only by 1 and itself.
What are the factors of 10067?
1, 10067.
What is 10067 in binary?
10011101010011 (hexadecimal 2753, octal 23523).
What is the square root of 10067?
About 100.3344.
Is 10067 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 10067?
10067 is a twin prime (10067 and 10069 are both prime); the 1235th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.