The number 6825
6825 is a composite number with 24 divisors. Its prime factorisation is 3 × × 7 × 13. Divisors (24): 1, 3, 5, 7, 13, 15, 21, 25, 35, 39, 65, 75, 91, 105, 175, 195 … 6825.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 6825: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.
- 2
6825 is composite. Its prime factorisation is
- 3
The divisors add up to 13888; without 6825 itself that is 7063, so 6825 is abundant (7063 is more than 6825). Euler's totient φ(6825) = 2880 numbers up to 6825 share no factor with it.
- 4
The digits of 6825 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 119 steps to reach 1.
LaTeX source of the formulas on this page
\[ 6825 = 3 \times 5^{2} \times 7 \times 13 \]6825 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 13888 |
| Euler totient φ(n) | 2880 |
| Square | 46580625 |
| Cube | 317912765625 |
| Square root | 82.613558 (= 5√273) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 119 |
| Scientific notation | 6.825 × |
6825 in other forms
| Form | Value |
|---|---|
| In words | six thousand eight hundred and twenty-five |
| Binary (base 2) | 1101010101001 |
| Octal (base 8) | 15251 |
| Hexadecimal (base 16) | 1AA9 |
| Base 3 | 100100210 |
| As time | 6825 seconds = 1 h 53 min 45 s |
Is 6825 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (6825 ÷ 3 = 2275) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (6825 ÷ 5 = 1365) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (6825 ÷ 7 = 975) | 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 1) | 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 | No (remainder 5) | 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 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 6825 a prime number?
No. 6825 = 3 × × 7 × 13, so it is divisible by 3.
What are the factors of 6825?
1, 3, 5, 7, 13, 15, 21, 25, 35, 39, 65, 75, 91, 105, 175, 195, 273, 325, 455, 525, 975, 1365, 2275, 6825.
What is 6825 in binary?
1101010101001 (hexadecimal 1AA9, octal 15251).
What is the square root of 6825?
About 82.6136, exactly 5√273.
Is 6825 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 6825?
6825 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.