The number 825
825 is a composite number with 12 divisors. Its prime factorisation is 3 × × 11. Divisors (12): 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 825: a Harshad number: divisible by its digit sum 15.
- 2
825 is composite. Its prime factorisation is
- 3
The divisors add up to 1488; without 825 itself that is 663, so 825 is deficient (663 is less than 825). Euler's totient φ(825) = 400 numbers up to 825 share no factor with it.
- 4
The digits of 825 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 134 steps to reach 1.
LaTeX source of the formulas on this page
\[ 825 = 3 \times 5^{2} \times 11 \]825 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1488 |
| Euler totient φ(n) | 400 |
| Square | 680625 |
| Cube | 561515625 |
| Square root | 28.722813 (= 5√33) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 134 |
| Scientific notation | 8.25 × |
825 in other forms
| Form | Value |
|---|---|
| In words | eight hundred and twenty-five |
| Roman numerals | DCCCXXV |
| Binary (base 2) | 1100111001 |
| Octal (base 8) | 1471 |
| Hexadecimal (base 16) | 339 |
| Base 3 | 1010120 |
| As time | 825 seconds = 13 min 45 s |
Is 825 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 (825 ÷ 3 = 275) | 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 (825 ÷ 5 = 165) | 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 | No (remainder 6) | 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 6) | 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 | Yes (825 ÷ 11 = 75) | 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 825 a prime number?
No. 825 = 3 × × 11, so it is divisible by 3.
What are the factors of 825?
1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825.
What is 825 in binary?
1100111001 (hexadecimal 339, octal 1471).
What is the square root of 825?
About 28.7228, exactly 5√33.
What is 825 in Roman numerals?
DCCCXXV.
Is 825 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 825?
825 is a Harshad number: divisible by its digit sum 15.