Number dictionary · Exact arithmetic
338: factors and number facts
three hundred thirty-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
- three hundred thirty-eight
- Roman numeral
- CCCXXXVIII
- Prime factorization
- 2 × 13^2
- Digital root
- 5
All factors of 338
A positive factor divides 338 with no remainder. In ascending order, the complete list is:
1, 2, 13, 26, 169, 338
Factor pairs
- 1 × 338 = 338
- 2 × 169 = 338
- 13 × 26 = 338
Each pair describes an arrangement of 338 items into equal rows. The pairs have different row and column counts; 338 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 6
- Sum of all divisors
- 549
- Sum excluding 338
- 211
- Classification
- deficient
338 is deficient because its proper divisors add to 211, which is less than 338.
Prime factorization of 338
338 = 2 × 13^2
Repeated division, step by step
- 338 ÷ 2 = 169
- 169 ÷ 13 = 13
- 13 ÷ 13 = 1
Multiply the prime divisors in these steps to reconstruct 338. An exponent records how many times the same prime occurs. The divisor-count calculation is (1 + 1) × (2 + 1) = 6.
The preceding prime is 337. The next larger prime is 347. The factor list above explains why 338 is composite.
Learn the factorization method338 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred thirty-eight |
| Roman numeral | CCCXXXVIII |
| Binary (base 2) | 101010010 |
| Octal (base 8) | 522 |
| Decimal (base 10) | 338 |
| Hexadecimal (base 16) | 152 |
Check the binary conversion
Read 101010010 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
256 + 64 + 16 + 2 = 338
Check the hexadecimal conversion
1 × 16^2 + 5 × 16^1 + 2 × 16^0 = 338
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 338
- 338 squared
- 338 × 338 = 114,244
- 338 cubed
- 338 × 338 × 338 = 38,614,472
- Square root
- ≈ 18.384776
- Simplified radical
- 13√2
338 lies between 324 (18²) and 361 (19²), so it is not a perfect square. It is not a perfect cube.
338 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 338.
Distinguish a square from a square rootMultiplication table for 338
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 | 169 | 0 | Yes |
| 3 | 112 | 2 | No |
| 4 | 84 | 2 | No |
| 5 | 67 | 3 | No |
| 6 | 56 | 2 | No |
| 7 | 48 | 2 | No |
| 8 | 42 | 2 | No |
| 9 | 37 | 5 | No |
| 10 | 33 | 8 | No |
| 11 | 30 | 8 | No |
| 12 | 28 | 2 | No |
For example, 338 = 7 × 48 + 2. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 338
338 contains 3 decimal digits. Its digit sum is 3 + 3 + 8 = 14.
- 338: 3 + 3 + 8 = 14
- 14: 1 + 4 = 5
The digital root is 5. Reversing its digits gives 833; 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, 338/100 simplifies to 169/50 by dividing both terms by their greatest common divisor, 2. Its decimal value is 3.38. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 338 and 12 is 2. Their least common multiple is 2028. The identity GCD × LCM = 338 × 12 = 4056 checks both results.
Work through GCF and LCMQuestions about 338
What are the factors of 338?
The positive factors are 1, 2, 13, 26, 169, 338. There are 6 factors, including 1 and 338.
Is 338 a prime number?
No. 338 is composite: 2 × 13^2 = 338.
How do you write 338 in Roman numerals?
338 is CCCXXXVIII in standard subtractive Roman numeral notation.
What is the binary representation of 338?
338 in decimal is 101010010 in base 2. Adding its active place values gives 256 + 64 + 16 + 2 = 338.
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 338
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 338 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.