The number 169
169 is a perfect square (13²). Its prime factorisation is . Divisors (3): 1, 13, 169.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 169: a perfect square (13²); the square of a prime (13²).
- 2
169 is composite. Its prime factorisation is
- 3
The divisors add up to 183; without 169 itself that is 14, so 169 is deficient (14 is less than 169). Euler's totient φ(169) = 156 numbers up to 169 share no factor with it.
- 4
The digits of 169 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 169 = 13^{2} \]169 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 3 |
| Sum of divisors | 183 |
| Euler totient φ(n) | 156 |
| Square | 28561 |
| Cube | 4826809 |
| Square root | 13 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 49 |
| Scientific notation | 1.69 × |
| Perfect power |
169 in other forms
| Form | Value |
|---|---|
| In words | one hundred and sixty-nine |
| Roman numerals | CLXIX |
| Binary (base 2) | 10101001 |
| Octal (base 8) | 251 |
| Hexadecimal (base 16) | A9 |
| Base 3 | 20021 |
| As time | 169 seconds = 2 min 49 s |
Is 169 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 1) | 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 169 a prime number?
No. 169 = , so it is divisible by 13.
What are the factors of 169?
1, 13, 169.
What is 169 in binary?
10101001 (hexadecimal A9, octal 251).
What is the square root of 169?
13, because 13 × 13 = 169.
What is 169 in Roman numerals?
CLXIX.
Is 169 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 169?
169 is a perfect square (13²); the square of a prime (13²).