Number dictionary · Exact arithmetic
825: factors and number facts
eight hundred twenty-five is an odd number and is composite. Its 12 positive divisors form 6 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- eight hundred twenty-five
- Roman numeral
- DCCCXXV
- Prime factorization
- 3 × 5^2 × 11
- Digital root
- 6
All factors of 825
A positive factor divides 825 with no remainder. In ascending order, the complete list is:
1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
Factor pairs
- 1 × 825 = 825
- 3 × 275 = 825
- 5 × 165 = 825
- 11 × 75 = 825
- 15 × 55 = 825
- 25 × 33 = 825
Each pair describes an arrangement of 825 items into equal rows. The pairs have different row and column counts; 825 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 12
- Sum of all divisors
- 1488
- Sum excluding 825
- 663
- Classification
- deficient
825 is deficient because its proper divisors add to 663, which is less than 825.
Prime factorization of 825
825 = 3 × 5^2 × 11
Repeated division, step by step
- 825 ÷ 3 = 275
- 275 ÷ 5 = 55
- 55 ÷ 5 = 11
- 11 ÷ 11 = 1
Multiply the prime divisors in these steps to reconstruct 825. An exponent records how many times the same prime occurs. The divisor-count calculation is (1 + 1) × (2 + 1) × (1 + 1) = 12.
The preceding prime is 823. The next larger prime is 827. The factor list above explains why 825 is composite.
Learn the factorization method825 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | eight hundred twenty-five |
| Roman numeral | DCCCXXV |
| Binary (base 2) | 1100111001 |
| Octal (base 8) | 1471 |
| Decimal (base 10) | 825 |
| Hexadecimal (base 16) | 339 |
Check the binary conversion
Read 1100111001 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
512 + 256 + 32 + 16 + 8 + 1 = 825
Check the hexadecimal conversion
3 × 16^2 + 3 × 16^1 + 9 × 16^0 = 825
Hexadecimal uses A through F for digit values 10 through 15. These notations represent the same quantity; changing the base does not change the integer.
Square, cube and square root of 825
- 825 squared
- 825 × 825 = 680,625
- 825 cubed
- 825 × 825 × 825 = 561,515,625
- Square root
- ≈ 28.722813
- Simplified radical
- 5√33
825 lies between 784 (28²) and 841 (29²), so it is not a perfect square. It is not a perfect cube.
825 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 825.
Distinguish a square from a square rootMultiplication table for 825
These are the first twelve positive multiples. Unlike the finite factor list, the sequence of multiples continues without an upper limit.
Divisibility checks
| Divide by | Whole quotient | Remainder | Divides exactly? |
|---|---|---|---|
| 2 | 412 | 1 | No |
| 3 | 275 | 0 | Yes |
| 4 | 206 | 1 | No |
| 5 | 165 | 0 | Yes |
| 6 | 137 | 3 | No |
| 7 | 117 | 6 | No |
| 8 | 103 | 1 | No |
| 9 | 91 | 6 | No |
| 10 | 82 | 5 | No |
| 11 | 75 | 0 | Yes |
| 12 | 68 | 9 | No |
For example, 825 = 7 × 117 + 6. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 825
825 contains 3 decimal digits. Its digit sum is 8 + 2 + 5 = 15.
- 825: 8 + 2 + 5 = 15
- 15: 1 + 5 = 6
The digital root is 6. Reversing its digits gives 528; it is not a decimal palindrome. Digit patterns depend on the notation being used.
Digital-root arithmetic always finishes at a single digit for a positive integer. Some numerology methods stop at 11, 22 or 33 instead; that is a separate interpretive convention.
Fractions and a worked comparison
As a fraction of 100, 825/100 simplifies to 33/4 by dividing both terms by their greatest common divisor, 25. Its decimal value is 8.25. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 825 and 12 is 3. Their least common multiple is 3300. The identity GCD × LCM = 825 × 12 = 9900 checks both results.
Work through GCF and LCMQuestions about 825
What are the factors of 825?
The positive factors are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825. There are 12 factors, including 1 and 825.
Is 825 a prime number?
No. 825 is composite: 3 × 5^2 × 11 = 825.
How do you write 825 in Roman numerals?
825 is DCCCXXV in standard subtractive Roman numeral notation.
What is the binary representation of 825?
825 in decimal is 1100111001 in base 2. Adding its active place values gives 512 + 256 + 32 + 16 + 8 + 1 = 825.
Methods and reference definitions
Number JD calculates each result from the integer on this page. Positive factors are enumerated in pairs; repeated division gives the prime factorization; place values verify base conversions. Decimal square roots are rounded to six places when irrational.
NUMBER JOURNAL / JD
A reflective note on 825
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 825 add to 15. That arithmetic result is separate from the cultural symbolism of the pattern. If this number matters to you, write down what you noticed and choose one grounded action rather than treating the sighting as a prediction.