Number dictionary · Exact arithmetic
724: factors and number facts
seven hundred twenty-four is an even number and is composite. Its 6 positive divisors form 3 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- seven hundred twenty-four
- Roman numeral
- DCCXXIV
- Prime factorization
- 2^2 × 181
- Digital root
- 4
All factors of 724
A positive factor divides 724 with no remainder. In ascending order, the complete list is:
1, 2, 4, 181, 362, 724
Factor pairs
- 1 × 724 = 724
- 2 × 362 = 724
- 4 × 181 = 724
Each pair describes an arrangement of 724 items into equal rows. The pairs have different row and column counts; 724 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 6
- Sum of all divisors
- 1274
- Sum excluding 724
- 550
- Classification
- deficient
724 is deficient because its proper divisors add to 550, which is less than 724.
Prime factorization of 724
724 = 2^2 × 181
Repeated division, step by step
- 724 ÷ 2 = 362
- 362 ÷ 2 = 181
- 181 ÷ 181 = 1
Multiply the prime divisors in these steps to reconstruct 724. An exponent records how many times the same prime occurs. The divisor-count calculation is (2 + 1) × (1 + 1) = 6.
The preceding prime is 719. The next larger prime is 727. The factor list above explains why 724 is composite.
Learn the factorization method724 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | seven hundred twenty-four |
| Roman numeral | DCCXXIV |
| Binary (base 2) | 1011010100 |
| Octal (base 8) | 1324 |
| Decimal (base 10) | 724 |
| Hexadecimal (base 16) | 2D4 |
Check the binary conversion
Read 1011010100 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
512 + 128 + 64 + 16 + 4 = 724
Check the hexadecimal conversion
2 × 16^2 + 13 × 16^1 + 4 × 16^0 = 724
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 724
- 724 squared
- 724 × 724 = 524,176
- 724 cubed
- 724 × 724 × 724 = 379,503,424
- Square root
- ≈ 26.907248
- Simplified radical
- 2√181
724 lies between 676 (26²) and 729 (27²), so it is not a perfect square. It is not a perfect cube.
724 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 724.
Distinguish a square from a square rootMultiplication table for 724
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 | 362 | 0 | Yes |
| 3 | 241 | 1 | No |
| 4 | 181 | 0 | Yes |
| 5 | 144 | 4 | No |
| 6 | 120 | 4 | No |
| 7 | 103 | 3 | No |
| 8 | 90 | 4 | No |
| 9 | 80 | 4 | No |
| 10 | 72 | 4 | No |
| 11 | 65 | 9 | No |
| 12 | 60 | 4 | No |
For example, 724 = 7 × 103 + 3. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 724
724 contains 3 decimal digits. Its digit sum is 7 + 2 + 4 = 13.
- 724: 7 + 2 + 4 = 13
- 13: 1 + 3 = 4
The digital root is 4. Reversing its digits gives 427; 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, 724/100 simplifies to 181/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 7.24. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 724 and 12 is 4. Their least common multiple is 2172. The identity GCD × LCM = 724 × 12 = 8688 checks both results.
Work through GCF and LCMQuestions about 724
What are the factors of 724?
The positive factors are 1, 2, 4, 181, 362, 724. There are 6 factors, including 1 and 724.
Is 724 a prime number?
No. 724 is composite: 2^2 × 181 = 724.
How do you write 724 in Roman numerals?
724 is DCCXXIV in standard subtractive Roman numeral notation.
What is the binary representation of 724?
724 in decimal is 1011010100 in base 2. Adding its active place values gives 512 + 128 + 64 + 16 + 4 = 724.
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 724
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 724 add to 13. 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.