Number dictionary · Exact arithmetic
238: factors and number facts
two hundred thirty-eight is an even number and is composite. Its 8 positive divisors form 4 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- two hundred thirty-eight
- Roman numeral
- CCXXXVIII
- Prime factorization
- 2 × 7 × 17
- Digital root
- 4
All factors of 238
A positive factor divides 238 with no remainder. In ascending order, the complete list is:
1, 2, 7, 14, 17, 34, 119, 238
Factor pairs
- 1 × 238 = 238
- 2 × 119 = 238
- 7 × 34 = 238
- 14 × 17 = 238
Each pair describes an arrangement of 238 items into equal rows. The pairs have different row and column counts; 238 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 8
- Sum of all divisors
- 432
- Sum excluding 238
- 194
- Classification
- deficient
238 is deficient because its proper divisors add to 194, which is less than 238.
Prime factorization of 238
238 = 2 × 7 × 17
Repeated division, step by step
- 238 ÷ 2 = 119
- 119 ÷ 7 = 17
- 17 ÷ 17 = 1
Multiply the prime divisors in these steps to reconstruct 238. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) × (1 + 1) = 8.
The preceding prime is 233. The next larger prime is 239. The factor list above explains why 238 is composite.
Learn the factorization method238 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | two hundred thirty-eight |
| Roman numeral | CCXXXVIII |
| Binary (base 2) | 11101110 |
| Octal (base 8) | 356 |
| Decimal (base 10) | 238 |
| Hexadecimal (base 16) | EE |
Check the binary conversion
Read 11101110 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
128 + 64 + 32 + 8 + 4 + 2 = 238
Check the hexadecimal conversion
14 × 16^1 + 14 × 16^0 = 238
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 238
- 238 squared
- 238 × 238 = 56,644
- 238 cubed
- 238 × 238 × 238 = 13,481,272
- Square root
- ≈ 15.427249
- Simplified radical
- √238
238 lies between 225 (15²) and 256 (16²), so it is not a perfect square. It is not a perfect cube.
238 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 238.
Distinguish a square from a square rootMultiplication table for 238
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 | 119 | 0 | Yes |
| 3 | 79 | 1 | No |
| 4 | 59 | 2 | No |
| 5 | 47 | 3 | No |
| 6 | 39 | 4 | No |
| 7 | 34 | 0 | Yes |
| 8 | 29 | 6 | No |
| 9 | 26 | 4 | No |
| 10 | 23 | 8 | No |
| 11 | 21 | 7 | No |
| 12 | 19 | 10 | No |
For example, 238 = 7 × 34 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 238
238 contains 3 decimal digits. Its digit sum is 2 + 3 + 8 = 13.
- 238: 2 + 3 + 8 = 13
- 13: 1 + 3 = 4
The digital root is 4. Reversing its digits gives 832; 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, 238/100 simplifies to 119/50 by dividing both terms by their greatest common divisor, 2. Its decimal value is 2.38. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 238 and 12 is 2. Their least common multiple is 1428. The identity GCD × LCM = 238 × 12 = 2856 checks both results.
Work through GCF and LCMQuestions about 238
What are the factors of 238?
The positive factors are 1, 2, 7, 14, 17, 34, 119, 238. There are 8 factors, including 1 and 238.
Is 238 a prime number?
No. 238 is composite: 2 × 7 × 17 = 238.
How do you write 238 in Roman numerals?
238 is CCXXXVIII in standard subtractive Roman numeral notation.
What is the binary representation of 238?
238 in decimal is 11101110 in base 2. Adding its active place values gives 128 + 64 + 32 + 8 + 4 + 2 = 238.
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 238
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 238 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.