The number 800
800 is a composite number with 18 divisors. Its prime factorisation is × . Divisors (18): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200 … 800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 800: a Harshad number: divisible by its digit sum 8.
- 2
800 is composite. Its prime factorisation is
- 3
The divisors add up to 1953; without 800 itself that is 1153, so 800 is abundant (1153 is more than 800). Euler's totient φ(800) = 320 numbers up to 800 share no factor with it.
- 4
The digits of 800 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 28 steps to reach 1.
LaTeX source of the formulas on this page
\[ 800 = 2^{5} \times 5^{2} \]800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 1953 |
| Euler totient φ(n) | 320 |
| Square | 640000 |
| Cube | 512000000 |
| Square root | 28.284271 (= 20√2) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 28 |
| Scientific notation | 8 × |
800 in other forms
| Form | Value |
|---|---|
| In words | eight hundred |
| Roman numerals | DCCC |
| Binary (base 2) | 1100100000 |
| Octal (base 8) | 1440 |
| Hexadecimal (base 16) | 320 |
| Base 3 | 1002122 |
| As time | 800 seconds = 13 min 20 s |
Is 800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (800 ÷ 2 = 400) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (800 ÷ 4 = 200) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (800 ÷ 5 = 160) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (800 ÷ 8 = 100) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (800 ÷ 10 = 80) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 800 a prime number?
No. 800 = × , so it is divisible by 2.
What are the factors of 800?
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800.
What is 800 in binary?
1100100000 (hexadecimal 320, octal 1440).
What is the square root of 800?
About 28.2843, exactly 20√2.
What is 800 in Roman numerals?
DCCC.
Is 800 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 800?
800 is a Harshad number: divisible by its digit sum 8.