The number 167
167 is the 39th prime number. Its only divisors are 1 and 167.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 167: the 39th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
167 is prime, so its only factors are 1 and 167. It is the 39th prime; the next prime is 173 and the one before is 163.
- 3
The divisors add up to 168; without 167 itself that is 1, so 167 is deficient (1 is less than 167). Euler's totient φ(167) = 166 numbers up to 167 share no factor with it.
- 4
The digits of 167 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 67 steps to reach 1.
167 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 168 |
| Euler totient φ(n) | 166 |
| Square | 27889 |
| Cube | 4657463 |
| Square root | 12.922848 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 67 |
| Scientific notation | 1.67 × |
167 in other forms
| Form | Value |
|---|---|
| In words | one hundred and sixty-seven |
| Roman numerals | CLXVII |
| Binary (base 2) | 10100111 |
| Octal (base 8) | 247 |
| Hexadecimal (base 16) | A7 |
| Base 3 | 20012 |
| As time | 167 seconds = 2 min 47 s |
Is 167 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 6) | 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 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 167 a prime number?
Yes. 167 is divisible only by 1 and itself.
What are the factors of 167?
1, 167.
What is 167 in binary?
10100111 (hexadecimal A7, octal 247).
What is the square root of 167?
About 12.9228.
What is 167 in Roman numerals?
CLXVII.
Is 167 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 167?
167 is the 39th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.