The number 171
171 is a triangular number: 1 + 2 + … + 18 = 171 and a palindrome: it reads 171 backwards too. Its prime factorisation is × 19. Divisors (6): 1, 3, 9, 19, 57, 171.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 171: a triangular number: 1 + 2 + … + 18 = 171; a palindrome: it reads 171 backwards too; a Harshad number: divisible by its digit sum 9.
- 2
171 is composite. Its prime factorisation is
- 3
The divisors add up to 260; without 171 itself that is 89, so 171 is deficient (89 is less than 171). Euler's totient φ(171) = 108 numbers up to 171 share no factor with it.
- 4
The digits of 171 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 124 steps to reach 1.
LaTeX source of the formulas on this page
\[ 171 = 3^{2} \times 19 \]171 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 260 |
| Euler totient φ(n) | 108 |
| Square | 29241 |
| Cube | 5000211 |
| Square root | 13.076697 (= 3√19) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 124 |
| Scientific notation | 1.71 × |
171 in other forms
| Form | Value |
|---|---|
| In words | one hundred and seventy-one |
| Roman numerals | CLXXI |
| Binary (base 2) | 10101011 |
| Octal (base 8) | 253 |
| Hexadecimal (base 16) | AB |
| Base 3 | 20100 |
| As time | 171 seconds = 2 min 51 s |
Is 171 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 | Yes (171 ÷ 3 = 57) | 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 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | Yes (171 ÷ 9 = 19) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 171 a prime number?
No. 171 = × 19, so it is divisible by 3.
What are the factors of 171?
1, 3, 9, 19, 57, 171.
What is 171 in binary?
10101011 (hexadecimal AB, octal 253).
What is the square root of 171?
About 13.0767, exactly 3√19.
What is 171 in Roman numerals?
CLXXI.
Is 171 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 171?
171 is a triangular number: 1 + 2 + … + 18 = 171; a palindrome: it reads 171 backwards too; a Harshad number: divisible by its digit sum 9.