Number dictionary · Exact arithmetic
824: factors and number facts
eight hundred twenty-four is an even number and is composite. Its 8 positive divisors form 4 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- eight hundred twenty-four
- Roman numeral
- DCCCXXIV
- Prime factorization
- 2^3 × 103
- Digital root
- 5
All factors of 824
A positive factor divides 824 with no remainder. In ascending order, the complete list is:
1, 2, 4, 8, 103, 206, 412, 824
Factor pairs
- 1 × 824 = 824
- 2 × 412 = 824
- 4 × 206 = 824
- 8 × 103 = 824
Each pair describes an arrangement of 824 items into equal rows. The pairs have different row and column counts; 824 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 8
- Sum of all divisors
- 1560
- Sum excluding 824
- 736
- Classification
- deficient
824 is deficient because its proper divisors add to 736, which is less than 824.
Prime factorization of 824
824 = 2^3 × 103
Repeated division, step by step
- 824 ÷ 2 = 412
- 412 ÷ 2 = 206
- 206 ÷ 2 = 103
- 103 ÷ 103 = 1
Multiply the prime divisors in these steps to reconstruct 824. An exponent records how many times the same prime occurs. The divisor-count calculation is (3 + 1) × (1 + 1) = 8.
The preceding prime is 823. The next larger prime is 827. The factor list above explains why 824 is composite.
Learn the factorization method824 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | eight hundred twenty-four |
| Roman numeral | DCCCXXIV |
| Binary (base 2) | 1100111000 |
| Octal (base 8) | 1470 |
| Decimal (base 10) | 824 |
| Hexadecimal (base 16) | 338 |
Check the binary conversion
Read 1100111000 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 = 824
Check the hexadecimal conversion
3 × 16^2 + 3 × 16^1 + 8 × 16^0 = 824
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 824
- 824 squared
- 824 × 824 = 678,976
- 824 cubed
- 824 × 824 × 824 = 559,476,224
- Square root
- ≈ 28.705400
- Simplified radical
- 2√206
824 lies between 784 (28²) and 841 (29²), so it is not a perfect square. It is not a perfect cube.
824 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 824.
Distinguish a square from a square rootMultiplication table for 824
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 | 0 | Yes |
| 3 | 274 | 2 | No |
| 4 | 206 | 0 | Yes |
| 5 | 164 | 4 | No |
| 6 | 137 | 2 | No |
| 7 | 117 | 5 | No |
| 8 | 103 | 0 | Yes |
| 9 | 91 | 5 | No |
| 10 | 82 | 4 | No |
| 11 | 74 | 10 | No |
| 12 | 68 | 8 | No |
For example, 824 = 7 × 117 + 5. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 824
824 contains 3 decimal digits. Its digit sum is 8 + 2 + 4 = 14.
- 824: 8 + 2 + 4 = 14
- 14: 1 + 4 = 5
The digital root is 5. Reversing its digits gives 428; 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, 824/100 simplifies to 206/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 8.24. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 824 and 12 is 4. Their least common multiple is 2472. The identity GCD × LCM = 824 × 12 = 9888 checks both results.
Work through GCF and LCMQuestions about 824
What are the factors of 824?
The positive factors are 1, 2, 4, 8, 103, 206, 412, 824. There are 8 factors, including 1 and 824.
Is 824 a prime number?
No. 824 is composite: 2^3 × 103 = 824.
How do you write 824 in Roman numerals?
824 is DCCCXXIV in standard subtractive Roman numeral notation.
What is the binary representation of 824?
824 in decimal is 1100111000 in base 2. Adding its active place values gives 512 + 256 + 32 + 16 + 8 = 824.
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 824
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 824 add to 14. 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.