Number dictionary · Exact arithmetic
744: factors and number facts
seven hundred forty-four is an even number and is composite. Its 16 positive divisors form 8 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- seven hundred forty-four
- Roman numeral
- DCCXLIV
- Prime factorization
- 2^3 × 3 × 31
- Digital root
- 6
All factors of 744
A positive factor divides 744 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372, 744
Factor pairs
- 1 × 744 = 744
- 2 × 372 = 744
- 3 × 248 = 744
- 4 × 186 = 744
- 6 × 124 = 744
- 8 × 93 = 744
- 12 × 62 = 744
- 24 × 31 = 744
Each pair describes an arrangement of 744 items into equal rows. The pairs have different row and column counts; 744 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 16
- Sum of all divisors
- 1920
- Sum excluding 744
- 1176
- Classification
- abundant
744 is abundant because its proper divisors add to 1176, which is greater than 744.
Prime factorization of 744
744 = 2^3 × 3 × 31
Repeated division, step by step
- 744 ÷ 2 = 372
- 372 ÷ 2 = 186
- 186 ÷ 2 = 93
- 93 ÷ 3 = 31
- 31 ÷ 31 = 1
Multiply the prime divisors in these steps to reconstruct 744. An exponent records how many times the same prime occurs. The divisor-count calculation is (3 + 1) × (1 + 1) × (1 + 1) = 16.
The preceding prime is 743. The next larger prime is 751. The factor list above explains why 744 is composite.
Learn the factorization method744 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | seven hundred forty-four |
| Roman numeral | DCCXLIV |
| Binary (base 2) | 1011101000 |
| Octal (base 8) | 1350 |
| Decimal (base 10) | 744 |
| Hexadecimal (base 16) | 2E8 |
Check the binary conversion
Read 1011101000 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 + 32 + 8 = 744
Check the hexadecimal conversion
2 × 16^2 + 14 × 16^1 + 8 × 16^0 = 744
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 744
- 744 squared
- 744 × 744 = 553,536
- 744 cubed
- 744 × 744 × 744 = 411,830,784
- Square root
- ≈ 27.276363
- Simplified radical
- 2√186
744 lies between 729 (27²) and 784 (28²), so it is not a perfect square. It is not a perfect cube.
744 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 744.
Distinguish a square from a square rootMultiplication table for 744
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 | 372 | 0 | Yes |
| 3 | 248 | 0 | Yes |
| 4 | 186 | 0 | Yes |
| 5 | 148 | 4 | No |
| 6 | 124 | 0 | Yes |
| 7 | 106 | 2 | No |
| 8 | 93 | 0 | Yes |
| 9 | 82 | 6 | No |
| 10 | 74 | 4 | No |
| 11 | 67 | 7 | No |
| 12 | 62 | 0 | Yes |
For example, 744 = 7 × 106 + 2. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 744
744 contains 3 decimal digits. Its digit sum is 7 + 4 + 4 = 15.
- 744: 7 + 4 + 4 = 15
- 15: 1 + 5 = 6
The digital root is 6. Reversing its digits gives 447; 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, 744/100 simplifies to 186/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 7.44. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 744 and 12 is 12. Their least common multiple is 744. The identity GCD × LCM = 744 × 12 = 8928 checks both results.
Work through GCF and LCMQuestions about 744
What are the factors of 744?
The positive factors are 1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372, 744. There are 16 factors, including 1 and 744.
Is 744 a prime number?
No. 744 is composite: 2^3 × 3 × 31 = 744.
How do you write 744 in Roman numerals?
744 is DCCXLIV in standard subtractive Roman numeral notation.
What is the binary representation of 744?
744 in decimal is 1011101000 in base 2. Adding its active place values gives 512 + 128 + 64 + 32 + 8 = 744.
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 744
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 744 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.