Number dictionary · Exact arithmetic
438: factors and number facts
four 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
- four hundred thirty-eight
- Roman numeral
- CDXXXVIII
- Prime factorization
- 2 × 3 × 73
- Digital root
- 6
All factors of 438
A positive factor divides 438 with no remainder. In ascending order, the complete list is:
1, 2, 3, 6, 73, 146, 219, 438
Factor pairs
- 1 × 438 = 438
- 2 × 219 = 438
- 3 × 146 = 438
- 6 × 73 = 438
Each pair describes an arrangement of 438 items into equal rows. The pairs have different row and column counts; 438 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 8
- Sum of all divisors
- 888
- Sum excluding 438
- 450
- Classification
- abundant
438 is abundant because its proper divisors add to 450, which is greater than 438.
Prime factorization of 438
438 = 2 × 3 × 73
Repeated division, step by step
- 438 ÷ 2 = 219
- 219 ÷ 3 = 73
- 73 ÷ 73 = 1
Multiply the prime divisors in these steps to reconstruct 438. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) × (1 + 1) = 8.
The preceding prime is 433. The next larger prime is 439. The factor list above explains why 438 is composite.
Learn the factorization method438 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | four hundred thirty-eight |
| Roman numeral | CDXXXVIII |
| Binary (base 2) | 110110110 |
| Octal (base 8) | 666 |
| Decimal (base 10) | 438 |
| Hexadecimal (base 16) | 1B6 |
Check the binary conversion
Read 110110110 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
256 + 128 + 32 + 16 + 4 + 2 = 438
Check the hexadecimal conversion
1 × 16^2 + 11 × 16^1 + 6 × 16^0 = 438
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 438
- 438 squared
- 438 × 438 = 191,844
- 438 cubed
- 438 × 438 × 438 = 84,027,672
- Square root
- ≈ 20.928450
- Simplified radical
- √438
438 lies between 400 (20²) and 441 (21²), so it is not a perfect square. It is not a perfect cube.
438 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 438.
Distinguish a square from a square rootMultiplication table for 438
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 | 219 | 0 | Yes |
| 3 | 146 | 0 | Yes |
| 4 | 109 | 2 | No |
| 5 | 87 | 3 | No |
| 6 | 73 | 0 | Yes |
| 7 | 62 | 4 | No |
| 8 | 54 | 6 | No |
| 9 | 48 | 6 | No |
| 10 | 43 | 8 | No |
| 11 | 39 | 9 | No |
| 12 | 36 | 6 | No |
For example, 438 = 7 × 62 + 4. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 438
438 contains 3 decimal digits. Its digit sum is 4 + 3 + 8 = 15.
- 438: 4 + 3 + 8 = 15
- 15: 1 + 5 = 6
The digital root is 6. Reversing its digits gives 834; 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, 438/100 simplifies to 219/50 by dividing both terms by their greatest common divisor, 2. Its decimal value is 4.38. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 438 and 12 is 6. Their least common multiple is 876. The identity GCD × LCM = 438 × 12 = 5256 checks both results.
Work through GCF and LCMQuestions about 438
What are the factors of 438?
The positive factors are 1, 2, 3, 6, 73, 146, 219, 438. There are 8 factors, including 1 and 438.
Is 438 a prime number?
No. 438 is composite: 2 × 3 × 73 = 438.
How do you write 438 in Roman numerals?
438 is CDXXXVIII in standard subtractive Roman numeral notation.
What is the binary representation of 438?
438 in decimal is 110110110 in base 2. Adding its active place values gives 256 + 128 + 32 + 16 + 4 + 2 = 438.
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 438
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 438 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.