The number 2140
2140 is a composite number with 12 divisors. Its prime factorisation is × 5 × 107. Divisors (12): 1, 2, 4, 5, 10, 20, 107, 214, 428, 535, 1070, 2140.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
2140 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
2140 is composite. Its prime factorisation is
- 3
The divisors add up to 4536; without 2140 itself that is 2396, so 2140 is abundant (2396 is more than 2140). Euler's totient φ(2140) = 848 numbers up to 2140 share no factor with it.
- 4
The digits of 2140 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 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2140 = 2^{2} \times 5 \times 107 \]2140 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 4536 |
| Euler totient φ(n) | 848 |
| Square | 4579600 |
| Cube | 9800344000 |
| Square root | 46.260134 (= 2√535) |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 24 |
| Scientific notation | 2.14 × |
2140 in other forms
| Form | Value |
|---|---|
| In words | two thousand one hundred and forty |
| Roman numerals | MMCXL |
| Binary (base 2) | 100001011100 |
| Octal (base 8) | 4134 |
| Hexadecimal (base 16) | 85C |
| Base 3 | 2221021 |
| As time | 2140 seconds = 35 min 40 s |
Is 2140 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2140 ÷ 2 = 1070) | 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 | Yes (2140 ÷ 4 = 535) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (2140 ÷ 5 = 428) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (2140 ÷ 10 = 214) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2140 a prime number?
No. 2140 = × 5 × 107, so it is divisible by 2.
What are the factors of 2140?
1, 2, 4, 5, 10, 20, 107, 214, 428, 535, 1070, 2140.
What is 2140 in binary?
100001011100 (hexadecimal 85C, octal 4134).
What is the square root of 2140?
About 46.2601, exactly 2√535.
What is 2140 in Roman numerals?
MMCXL.
Is 2140 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 2140?
It is a composite number with 12 divisors.