The number 2190
2190 is a composite number with 16 divisors. Its prime factorisation is 2 × 3 × 5 × 73. Divisors (16): 1, 2, 3, 5, 6, 10, 15, 30, 73, 146, 219, 365, 438, 730, 1095, 2190.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2190: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
2190 is composite. Its prime factorisation is
- 3
The divisors add up to 5328; without 2190 itself that is 3138, so 2190 is abundant (3138 is more than 2190). Euler's totient φ(2190) = 576 numbers up to 2190 share no factor with it.
- 4
The digits of 2190 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 76 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2190 = 2 \times 3 \times 5 \times 73 \]
2190 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 5328 |
| Euler totient φ(n) | 576 |
| Square | 4796100 |
| Cube | 10503459000 |
| Square root | 46.797436 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 76 |
| Scientific notation | 2.19 × |
2190 in other forms
| Form | Value |
|---|---|
| In words | two thousand one hundred and ninety |
| Roman numerals | MMCXC |
| Binary (base 2) | 100010001110 |
| Octal (base 8) | 4216 |
| Hexadecimal (base 16) | 88E |
| Base 3 | 10000010 |
| As time | 2190 seconds = 36 min 30 s |
Is 2190 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2190 ÷ 2 = 1095) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2190 ÷ 3 = 730) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (2190 ÷ 5 = 438) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (2190 ÷ 6 = 365) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (2190 ÷ 10 = 219) | 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 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2190 a prime number?
No. 2190 = 2 × 3 × 5 × 73, so it is divisible by 2.
What are the factors of 2190?
1, 2, 3, 5, 6, 10, 15, 30, 73, 146, 219, 365, 438, 730, 1095, 2190.
What is 2190 in binary?
100010001110 (hexadecimal 88E, octal 4216).
What is the square root of 2190?
About 46.7974.
What is 2190 in Roman numerals?
MMCXC.
Is 2190 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 2190?
2190 is a happy number: repeatedly adding the squares of its digits reaches 1.