The number 2080
2080 is a triangular number: 1 + 2 + … + 64 = 2080. Its prime factorisation is × 5 × 13. Divisors (24): 1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 32, 40, 52, 65, 80, 104 … 2080.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2080: a triangular number: 1 + 2 + … + 64 = 2080; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.
- 2
2080 is composite. Its prime factorisation is
- 3
The divisors add up to 5292; without 2080 itself that is 3212, so 2080 is abundant (3212 is more than 2080). Euler's totient φ(2080) = 768 numbers up to 2080 share no factor with it.
- 4
The digits of 2080 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2080 = 2^{5} \times 5 \times 13 \]2080 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 5292 |
| Euler totient φ(n) | 768 |
| Square | 4326400 |
| Cube | 8998912000 |
| Square root | 45.607017 (= 4√130) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 32 |
| Scientific notation | 2.08 × |
2080 in other forms
| Form | Value |
|---|---|
| In words | two thousand and eighty |
| Roman numerals | MMLXXX |
| Binary (base 2) | 100000100000 |
| Octal (base 8) | 4040 |
| Hexadecimal (base 16) | 820 |
| Base 3 | 2212001 |
| As time | 2080 seconds = 34 min 40 s |
Is 2080 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2080 ÷ 2 = 1040) | 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 (2080 ÷ 4 = 520) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (2080 ÷ 5 = 416) | 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 1) | 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 (2080 ÷ 8 = 260) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (2080 ÷ 10 = 208) | 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 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2080 a prime number?
No. 2080 = × 5 × 13, so it is divisible by 2.
What are the factors of 2080?
1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 32, 40, 52, 65, 80, 104, 130, 160, 208, 260, 416, 520, 1040, 2080.
What is 2080 in binary?
100000100000 (hexadecimal 820, octal 4040).
What is the square root of 2080?
About 45.6070, exactly 4√130.
What is 2080 in Roman numerals?
MMLXXX.
Is 2080 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 2080?
2080 is a triangular number: 1 + 2 + … + 64 = 2080; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.