The number 72167
72167 is a twin prime (72167 and 72169 are both prime) and the 7143rd prime number. Its only divisors are 1 and 72167.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72167: a twin prime (72167 and 72169 are both prime); the 7143rd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
72167 is prime, so its only factors are 1 and 72167. It is the 7143rd prime; the next prime is 72169 and the one before is 72161.
- 3
The divisors add up to 72168; without 72167 itself that is 1, so 72167 is deficient (1 is less than 72167). Euler's totient φ(72167) = 72166 numbers up to 72167 share no factor with it.
- 4
The digits of 72167 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
72167 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 72168 |
| Euler totient φ(n) | 72166 |
| Square | 5208075889 |
| Cube | 375851212681463 |
| Square root | 268.639163 |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 68 |
| Scientific notation | 7.2167 × |
72167 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand one hundred and sixty-seven |
| Binary (base 2) | 10001100111100111 |
| Octal (base 8) | 214747 |
| Hexadecimal (base 16) | 119E7 |
| Base 3 | 10122222212 |
| As time | 72167 seconds = 20 h 2 min 47 s |
Is 72167 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 4) | 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 7) | 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 7) | 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 72167 a prime number?
Yes. 72167 is divisible only by 1 and itself.
What are the factors of 72167?
1, 72167.
What is 72167 in binary?
10001100111100111 (hexadecimal 119E7, octal 214747).
What is the square root of 72167?
About 268.6392.
Is 72167 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 72167?
72167 is a twin prime (72167 and 72169 are both prime); the 7143rd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.