Number dictionary · Exact arithmetic
788: factors and number facts
seven hundred eighty-eight 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 eighty-eight
- Roman numeral
- DCCLXXXVIII
- Prime factorization
- 2^2 × 197
- Digital root
- 5
All factors of 788
A positive factor divides 788 with no remainder. In ascending order, the complete list is:
1, 2, 4, 197, 394, 788
Factor pairs
- 1 × 788 = 788
- 2 × 394 = 788
- 4 × 197 = 788
Each pair describes an arrangement of 788 items into equal rows. The pairs have different row and column counts; 788 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 6
- Sum of all divisors
- 1386
- Sum excluding 788
- 598
- Classification
- deficient
788 is deficient because its proper divisors add to 598, which is less than 788.
Prime factorization of 788
788 = 2^2 × 197
Repeated division, step by step
- 788 ÷ 2 = 394
- 394 ÷ 2 = 197
- 197 ÷ 197 = 1
Multiply the prime divisors in these steps to reconstruct 788. An exponent records how many times the same prime occurs. The divisor-count calculation is (2 + 1) × (1 + 1) = 6.
The preceding prime is 787. The next larger prime is 797. The factor list above explains why 788 is composite.
Learn the factorization method788 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | seven hundred eighty-eight |
| Roman numeral | DCCLXXXVIII |
| Binary (base 2) | 1100010100 |
| Octal (base 8) | 1424 |
| Decimal (base 10) | 788 |
| Hexadecimal (base 16) | 314 |
Check the binary conversion
Read 1100010100 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 + 16 + 4 = 788
Check the hexadecimal conversion
3 × 16^2 + 1 × 16^1 + 4 × 16^0 = 788
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 788
- 788 squared
- 788 × 788 = 620,944
- 788 cubed
- 788 × 788 × 788 = 489,303,872
- Square root
- ≈ 28.071338
- Simplified radical
- 2√197
788 lies between 784 (28²) and 841 (29²), so it is not a perfect square. It is not a perfect cube.
788 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 788.
Distinguish a square from a square rootMultiplication table for 788
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 | 394 | 0 | Yes |
| 3 | 262 | 2 | No |
| 4 | 197 | 0 | Yes |
| 5 | 157 | 3 | No |
| 6 | 131 | 2 | No |
| 7 | 112 | 4 | No |
| 8 | 98 | 4 | No |
| 9 | 87 | 5 | No |
| 10 | 78 | 8 | No |
| 11 | 71 | 7 | No |
| 12 | 65 | 8 | No |
For example, 788 = 7 × 112 + 4. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 788
788 contains 3 decimal digits. Its digit sum is 7 + 8 + 8 = 23.
- 788: 7 + 8 + 8 = 23
- 23: 2 + 3 = 5
The digital root is 5. Reversing its digits gives 887; 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, 788/100 simplifies to 197/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 7.88. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 788 and 12 is 4. Their least common multiple is 2364. The identity GCD × LCM = 788 × 12 = 9456 checks both results.
Work through GCF and LCMQuestions about 788
What are the factors of 788?
The positive factors are 1, 2, 4, 197, 394, 788. There are 6 factors, including 1 and 788.
Is 788 a prime number?
No. 788 is composite: 2^2 × 197 = 788.
How do you write 788 in Roman numerals?
788 is DCCLXXXVIII in standard subtractive Roman numeral notation.
What is the binary representation of 788?
788 in decimal is 1100010100 in base 2. Adding its active place values gives 512 + 256 + 16 + 4 = 788.
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 788
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 788 add to 23. 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.