The number 2340
2340 is a composite number with 36 divisors. Its prime factorisation is × × 5 × 13. Divisors (36): 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 26, 30, 36 … 2340.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2340: a Harshad number: divisible by its digit sum 9.
- 2
2340 is composite. Its prime factorisation is
- 3
The divisors add up to 7644; without 2340 itself that is 5304, so 2340 is abundant (5304 is more than 2340). Euler's totient φ(2340) = 576 numbers up to 2340 share no factor with it.
- 4
The digits of 2340 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 58 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2340 = 2^{2} \times 3^{2} \times 5 \times 13 \]2340 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 7644 |
| Euler totient φ(n) | 576 |
| Square | 5475600 |
| Cube | 12812904000 |
| Square root | 48.373546 (= 6√65) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 58 |
| Scientific notation | 2.34 × |
2340 in other forms
| Form | Value |
|---|---|
| In words | two thousand three hundred and forty |
| Roman numerals | MMCCCXL |
| Binary (base 2) | 100100100100 |
| Octal (base 8) | 4444 |
| Hexadecimal (base 16) | 924 |
| Base 3 | 10012200 |
| As time | 2340 seconds = 39 min 0 s |
Is 2340 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2340 ÷ 2 = 1170) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2340 ÷ 3 = 780) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2340 ÷ 4 = 585) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (2340 ÷ 5 = 468) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (2340 ÷ 6 = 390) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (2340 ÷ 9 = 260) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (2340 ÷ 10 = 234) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (2340 ÷ 12 = 195) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2340 a prime number?
No. 2340 = × × 5 × 13, so it is divisible by 2.
What are the factors of 2340?
1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 26, 30, 36, 39, 45, 52, 60, 65, 78, 90, 117, 130, 156, 180, 195, 234, 260, 390, 468, 585, 780, 1170, 2340.
What is 2340 in binary?
100100100100 (hexadecimal 924, octal 4444).
What is the square root of 2340?
About 48.3735, exactly 6√65.
What is 2340 in Roman numerals?
MMCCCXL.
Is 2340 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 2340?
2340 is a Harshad number: divisible by its digit sum 9.