The number 2113
2113 is a twin prime (2111 and 2113 are both prime) and the 319th prime number. Its only divisors are 1 and 2113.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2113: a twin prime (2111 and 2113 are both prime); the 319th prime number.
- 2
2113 is prime, so its only factors are 1 and 2113. It is the 319th prime; the next prime is 2129 and the one before is 2111.
- 3
The divisors add up to 2114; without 2113 itself that is 1, so 2113 is deficient (1 is less than 2113). Euler's totient φ(2113) = 2112 numbers up to 2113 share no factor with it.
- 4
The digits of 2113 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 81 steps to reach 1.
2113 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 2114 |
| Euler totient φ(n) | 2112 |
| Square | 4464769 |
| Cube | 9434056897 |
| Square root | 45.967380 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 81 |
| Scientific notation | 2.113 × |
2113 in other forms
| Form | Value |
|---|---|
| In words | two thousand one hundred and thirteen |
| Roman numerals | MMCXIII |
| Binary (base 2) | 100001000001 |
| Octal (base 8) | 4101 |
| Hexadecimal (base 16) | 841 |
| Base 3 | 2220021 |
| As time | 2113 seconds = 35 min 13 s |
Is 2113 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 3) | 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 6) | 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 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | 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 2113 a prime number?
Yes. 2113 is divisible only by 1 and itself.
What are the factors of 2113?
1, 2113.
What is 2113 in binary?
100001000001 (hexadecimal 841, octal 4101).
What is the square root of 2113?
About 45.9674.
What is 2113 in Roman numerals?
MMCXIII.
Is 2113 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 2113?
2113 is a twin prime (2111 and 2113 are both prime); the 319th prime number.