The number 189
189 is a binary palindrome (10111101). Its prime factorisation is × 7. Divisors (8): 1, 3, 7, 9, 21, 27, 63, 189.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 189: a binary palindrome (10111101).
- 2
189 is composite. Its prime factorisation is
- 3
The divisors add up to 320; without 189 itself that is 131, so 189 is deficient (131 is less than 189). Euler's totient φ(189) = 108 numbers up to 189 share no factor with it.
- 4
The digits of 189 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 106 steps to reach 1.
LaTeX source of the formulas on this page
\[ 189 = 3^{3} \times 7 \]189 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 320 |
| Euler totient φ(n) | 108 |
| Square | 35721 |
| Cube | 6751269 |
| Square root | 13.747727 (= 3√21) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 106 |
| Scientific notation | 1.89 × |
189 in other forms
| Form | Value |
|---|---|
| In words | one hundred and eighty-nine |
| Roman numerals | CLXXXIX |
| Binary (base 2) | 10111101 |
| Octal (base 8) | 275 |
| Hexadecimal (base 16) | BD |
| Base 3 | 21000 |
| As time | 189 seconds = 3 min 9 s |
Is 189 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 (189 ÷ 3 = 63) | 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 4) | 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 | Yes (189 ÷ 7 = 27) | 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 | Yes (189 ÷ 9 = 21) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 189 a prime number?
No. 189 = × 7, so it is divisible by 3.
What are the factors of 189?
1, 3, 7, 9, 21, 27, 63, 189.
What is 189 in binary?
10111101 (hexadecimal BD, octal 275).
What is the square root of 189?
About 13.7477, exactly 3√21.
What is 189 in Roman numerals?
CLXXXIX.
Is 189 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 189?
189 is a binary palindrome (10111101).