The number 109
109 is a twin prime (107 and 109 are both prime) and the 29th prime number. Its only divisors are 1 and 109.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 109: a twin prime (107 and 109 are both prime); the 29th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
109 is prime, so its only factors are 1 and 109. It is the 29th prime; the next prime is 113 and the one before is 107.
- 3
The divisors add up to 110; without 109 itself that is 1, so 109 is deficient (1 is less than 109). Euler's totient φ(109) = 108 numbers up to 109 share no factor with it.
- 4
The digits of 109 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 113 steps to reach 1.
109 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 110 |
| Euler totient φ(n) | 108 |
| Square | 11881 |
| Cube | 1295029 |
| Square root | 10.440307 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 113 |
| Scientific notation | 1.09 × |
109 in other forms
| Form | Value |
|---|---|
| In words | one hundred and nine |
| Roman numerals | CIX |
| Binary (base 2) | 1101101 |
| Octal (base 8) | 155 |
| Hexadecimal (base 16) | 6D |
| Base 3 | 11001 |
| As time | 109 seconds = 1 min 49 s |
Is 109 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 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 1) | 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 10) | 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 109 a prime number?
Yes. 109 is divisible only by 1 and itself.
What are the factors of 109?
1, 109.
What is 109 in binary?
1101101 (hexadecimal 6D, octal 155).
What is the square root of 109?
About 10.4403.
What is 109 in Roman numerals?
CIX.
Is 109 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 109?
109 is a twin prime (107 and 109 are both prime); the 29th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.