The number 2040
2040 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 17. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40 … 2040.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2040: a Harshad number: divisible by its digit sum 6.
- 2
2040 is composite. Its prime factorisation is
- 3
The divisors add up to 6480; without 2040 itself that is 4440, so 2040 is abundant (4440 is more than 2040). Euler's totient φ(2040) = 512 numbers up to 2040 share no factor with it.
- 4
The digits of 2040 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2040 = 2^{3} \times 3 \times 5 \times 17 \]2040 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 6480 |
| Euler totient φ(n) | 512 |
| Square | 4161600 |
| Cube | 8489664000 |
| Square root | 45.166359 (= 2√510) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 50 |
| Scientific notation | 2.04 × |
2040 in other forms
| Form | Value |
|---|---|
| In words | two thousand and forty |
| Roman numerals | MMXL |
| Binary (base 2) | 11111111000 |
| Octal (base 8) | 3770 |
| Hexadecimal (base 16) | 7F8 |
| Base 3 | 2210120 |
| As time | 2040 seconds = 34 min 0 s |
Is 2040 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2040 ÷ 2 = 1020) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2040 ÷ 3 = 680) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2040 ÷ 4 = 510) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (2040 ÷ 5 = 408) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (2040 ÷ 6 = 340) | 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 | Yes (2040 ÷ 8 = 255) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (2040 ÷ 10 = 204) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (2040 ÷ 12 = 170) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2040 a prime number?
No. 2040 = × 3 × 5 × 17, so it is divisible by 2.
What are the factors of 2040?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40, 51, 60, 68, 85, 102, 120, 136, 170, 204, 255, 340, 408, 510, 680, 1020, 2040.
What is 2040 in binary?
11111111000 (hexadecimal 7F8, octal 3770).
What is the square root of 2040?
About 45.1664, exactly 2√510.
What is 2040 in Roman numerals?
MMXL.
Is 2040 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 2040?
2040 is a Harshad number: divisible by its digit sum 6.