The number 165
165 is a binary palindrome (10100101). Its prime factorisation is 3 × 5 × 11. Divisors (8): 1, 3, 5, 11, 15, 33, 55, 165.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 165: a binary palindrome (10100101).
- 2
165 is composite. Its prime factorisation is
- 3
The divisors add up to 288; without 165 itself that is 123, so 165 is deficient (123 is less than 165). Euler's totient φ(165) = 80 numbers up to 165 share no factor with it.
- 4
The digits of 165 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 111 steps to reach 1.
LaTeX source of the formulas on this page
\[ 165 = 3 \times 5 \times 11 \]
165 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 288 |
| Euler totient φ(n) | 80 |
| Square | 27225 |
| Cube | 4492125 |
| Square root | 12.845233 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 111 |
| Scientific notation | 1.65 × |
165 in other forms
| Form | Value |
|---|---|
| In words | one hundred and sixty-five |
| Roman numerals | CLXV |
| Binary (base 2) | 10100101 |
| Octal (base 8) | 245 |
| Hexadecimal (base 16) | A5 |
| Base 3 | 20010 |
| As time | 165 seconds = 2 min 45 s |
Is 165 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 (165 ÷ 3 = 55) | 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 | Yes (165 ÷ 5 = 33) | 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 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (165 ÷ 11 = 15) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 165 a prime number?
No. 165 = 3 × 5 × 11, so it is divisible by 3.
What are the factors of 165?
1, 3, 5, 11, 15, 33, 55, 165.
What is 165 in binary?
10100101 (hexadecimal A5, octal 245).
What is the square root of 165?
About 12.8452.
What is 165 in Roman numerals?
CLXV.
Is 165 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 165?
165 is a binary palindrome (10100101).