The number 173
173 is the 40th prime number. Its only divisors are 1 and 173.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 173: the 40th prime number.
- 2
173 is prime, so its only factors are 1 and 173. It is the 40th prime; the next prime is 179 and the one before is 167.
- 3
The divisors add up to 174; without 173 itself that is 1, so 173 is deficient (1 is less than 173). Euler's totient φ(173) = 172 numbers up to 173 share no factor with it.
- 4
The digits of 173 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 31 steps to reach 1.
173 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 174 |
| Euler totient φ(n) | 172 |
| Square | 29929 |
| Cube | 5177717 |
| Square root | 13.152946 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 31 |
| Scientific notation | 1.73 × |
173 in other forms
| Form | Value |
|---|---|
| In words | one hundred and seventy-three |
| Roman numerals | CLXXIII |
| Binary (base 2) | 10101101 |
| Octal (base 8) | 255 |
| Hexadecimal (base 16) | AD |
| Base 3 | 20102 |
| As time | 173 seconds = 2 min 53 s |
Is 173 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 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | 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 5) | 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 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | 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 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 173 a prime number?
Yes. 173 is divisible only by 1 and itself.
What are the factors of 173?
1, 173.
What is 173 in binary?
10101101 (hexadecimal AD, octal 255).
What is the square root of 173?
About 13.1529.
What is 173 in Roman numerals?
CLXXIII.
Is 173 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 173?
173 is the 40th prime number.