The number 2800
2800 is a composite number with 30 divisors. Its prime factorisation is × × 7. Divisors (30): 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56 … 2800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2800: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.
- 2
2800 is composite. Its prime factorisation is
- 3
The divisors add up to 7688; without 2800 itself that is 4888, so 2800 is abundant (4888 is more than 2800). Euler's totient φ(2800) = 960 numbers up to 2800 share no factor with it.
- 4
The digits of 2800 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 84 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2800 = 2^{4} \times 5^{2} \times 7 \]2800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 7688 |
| Euler totient φ(n) | 960 |
| Square | 7840000 |
| Cube | 21952000000 |
| Square root | 52.915026 (= 20√7) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 84 |
| Scientific notation | 2.8 × |
2800 in other forms
| Form | Value |
|---|---|
| In words | two thousand eight hundred |
| Roman numerals | MMDCCC |
| Binary (base 2) | 101011110000 |
| Octal (base 8) | 5360 |
| Hexadecimal (base 16) | AF0 |
| Base 3 | 10211201 |
| As time | 2800 seconds = 46 min 40 s |
Is 2800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2800 ÷ 2 = 1400) | 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 (2800 ÷ 4 = 700) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (2800 ÷ 5 = 560) | 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 | Yes (2800 ÷ 7 = 400) | 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 (2800 ÷ 8 = 350) | 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 (2800 ÷ 10 = 280) | 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 2800 a prime number?
No. 2800 = × × 7, so it is divisible by 2.
What are the factors of 2800?
1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, 2800.
What is 2800 in binary?
101011110000 (hexadecimal AF0, octal 5360).
What is the square root of 2800?
About 52.9150, exactly 20√7.
What is 2800 in Roman numerals?
MMDCCC.
Is 2800 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 2800?
2800 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.