The number 113
113 is the 30th prime number. Its only divisors are 1 and 113.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 113: the 30th prime number.
- 2
113 is prime, so its only factors are 1 and 113. It is the 30th prime; the next prime is 127 and the one before is 109.
- 3
The divisors add up to 114; without 113 itself that is 1, so 113 is deficient (1 is less than 113). Euler's totient φ(113) = 112 numbers up to 113 share no factor with it.
- 4
The digits of 113 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 12 steps to reach 1.
113 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 114 |
| Euler totient φ(n) | 112 |
| Square | 12769 |
| Cube | 1442897 |
| Square root | 10.630146 |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 12 |
| Scientific notation | 1.13 × |
113 in other forms
| Form | Value |
|---|---|
| In words | one hundred and thirteen |
| Roman numerals | CXIII |
| Binary (base 2) | 1110001 |
| Octal (base 8) | 161 |
| Hexadecimal (base 16) | 71 |
| Base 3 | 11012 |
| As time | 113 seconds = 1 min 53 s |
Is 113 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 2) | 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 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 5) | 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 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 113 a prime number?
Yes. 113 is divisible only by 1 and itself.
What are the factors of 113?
1, 113.
What is 113 in binary?
1110001 (hexadecimal 71, octal 161).
What is the square root of 113?
About 10.6301.
What is 113 in Roman numerals?
CXIII.
Is 113 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 113?
113 is the 30th prime number.