Number dictionary · Exact arithmetic
738: factors and number facts
seven hundred thirty-eight is an even number and is composite. Its 12 positive divisors form 6 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- seven hundred thirty-eight
- Roman numeral
- DCCXXXVIII
- Prime factorization
- 2 × 3^2 × 41
- Digital root
- 9
All factors of 738
A positive factor divides 738 with no remainder. In ascending order, the complete list is:
1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738
Factor pairs
- 1 × 738 = 738
- 2 × 369 = 738
- 3 × 246 = 738
- 6 × 123 = 738
- 9 × 82 = 738
- 18 × 41 = 738
Each pair describes an arrangement of 738 items into equal rows. The pairs have different row and column counts; 738 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 12
- Sum of all divisors
- 1638
- Sum excluding 738
- 900
- Classification
- abundant
738 is abundant because its proper divisors add to 900, which is greater than 738.
Prime factorization of 738
738 = 2 × 3^2 × 41
Repeated division, step by step
- 738 ÷ 2 = 369
- 369 ÷ 3 = 123
- 123 ÷ 3 = 41
- 41 ÷ 41 = 1
Multiply the prime divisors in these steps to reconstruct 738. 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 733. The next larger prime is 739. The factor list above explains why 738 is composite.
Learn the factorization method738 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | seven hundred thirty-eight |
| Roman numeral | DCCXXXVIII |
| Binary (base 2) | 1011100010 |
| Octal (base 8) | 1342 |
| Decimal (base 10) | 738 |
| Hexadecimal (base 16) | 2E2 |
Check the binary conversion
Read 1011100010 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 + 2 = 738
Check the hexadecimal conversion
2 × 16^2 + 14 × 16^1 + 2 × 16^0 = 738
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 738
- 738 squared
- 738 × 738 = 544,644
- 738 cubed
- 738 × 738 × 738 = 401,947,272
- Square root
- ≈ 27.166155
- Simplified radical
- 3√82
738 lies between 729 (27²) and 784 (28²), so it is not a perfect square. It is not a perfect cube.
738 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 738.
Distinguish a square from a square rootMultiplication table for 738
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 | 369 | 0 | Yes |
| 3 | 246 | 0 | Yes |
| 4 | 184 | 2 | No |
| 5 | 147 | 3 | No |
| 6 | 123 | 0 | Yes |
| 7 | 105 | 3 | No |
| 8 | 92 | 2 | No |
| 9 | 82 | 0 | Yes |
| 10 | 73 | 8 | No |
| 11 | 67 | 1 | No |
| 12 | 61 | 6 | No |
For example, 738 = 7 × 105 + 3. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 738
738 contains 3 decimal digits. Its digit sum is 7 + 3 + 8 = 18.
- 738: 7 + 3 + 8 = 18
- 18: 1 + 8 = 9
The digital root is 9. Reversing its digits gives 837; 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, 738/100 simplifies to 369/50 by dividing both terms by their greatest common divisor, 2. Its decimal value is 7.38. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 738 and 12 is 6. Their least common multiple is 1476. The identity GCD × LCM = 738 × 12 = 8856 checks both results.
Work through GCF and LCMQuestions about 738
What are the factors of 738?
The positive factors are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738. There are 12 factors, including 1 and 738.
Is 738 a prime number?
No. 738 is composite: 2 × 3^2 × 41 = 738.
How do you write 738 in Roman numerals?
738 is DCCXXXVIII in standard subtractive Roman numeral notation.
What is the binary representation of 738?
738 in decimal is 1011100010 in base 2. Adding its active place values gives 512 + 128 + 64 + 32 + 2 = 738.
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 738
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 738 add to 18. 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.