The number 2313
2313 is a binary palindrome (100100001001). Its prime factorisation is × 257. Divisors (6): 1, 3, 9, 257, 771, 2313.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2313: a binary palindrome (100100001001); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
2313 is composite. Its prime factorisation is
- 3
The divisors add up to 3354; without 2313 itself that is 1041, so 2313 is deficient (1041 is less than 2313). Euler's totient φ(2313) = 1536 numbers up to 2313 share no factor with it.
- 4
The digits of 2313 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2313 = 3^{2} \times 257 \]2313 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 3354 |
| Euler totient φ(n) | 1536 |
| Square | 5349969 |
| Cube | 12374478297 |
| Square root | 48.093659 (= 3√257) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 107 |
| Scientific notation | 2.313 × |
2313 in other forms
| Form | Value |
|---|---|
| In words | two thousand three hundred and thirteen |
| Roman numerals | MMCCCXIII |
| Binary (base 2) | 100100001001 |
| Octal (base 8) | 4411 |
| Hexadecimal (base 16) | 909 |
| Base 3 | 10011200 |
| As time | 2313 seconds = 38 min 33 s |
Is 2313 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 (2313 ÷ 3 = 771) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | Yes (2313 ÷ 9 = 257) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2313 a prime number?
No. 2313 = × 257, so it is divisible by 3.
What are the factors of 2313?
1, 3, 9, 257, 771, 2313.
What is 2313 in binary?
100100001001 (hexadecimal 909, octal 4411).
What is the square root of 2313?
About 48.0937, exactly 3√257.
What is 2313 in Roman numerals?
MMCCCXIII.
Is 2313 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 2313?
2313 is a binary palindrome (100100001001); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.