Number dictionary · Exact arithmetic
342: factors and number facts
three hundred forty-two 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
- three hundred forty-two
- Roman numeral
- CCCXLII
- Prime factorization
- 2 × 3^2 × 19
- Digital root
- 9
All factors of 342
A positive factor divides 342 with no remainder. In ascending order, the complete list is:
1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
Factor pairs
- 1 × 342 = 342
- 2 × 171 = 342
- 3 × 114 = 342
- 6 × 57 = 342
- 9 × 38 = 342
- 18 × 19 = 342
Each pair describes an arrangement of 342 items into equal rows. The pairs have different row and column counts; 342 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 12
- Sum of all divisors
- 780
- Sum excluding 342
- 438
- Classification
- abundant
342 is abundant because its proper divisors add to 438, which is greater than 342.
Prime factorization of 342
342 = 2 × 3^2 × 19
Repeated division, step by step
- 342 ÷ 2 = 171
- 171 ÷ 3 = 57
- 57 ÷ 3 = 19
- 19 ÷ 19 = 1
Multiply the prime divisors in these steps to reconstruct 342. 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 337. The next larger prime is 347. The factor list above explains why 342 is composite.
Learn the factorization method342 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred forty-two |
| Roman numeral | CCCXLII |
| Binary (base 2) | 101010110 |
| Octal (base 8) | 526 |
| Decimal (base 10) | 342 |
| Hexadecimal (base 16) | 156 |
Check the binary conversion
Read 101010110 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 + 4 + 2 = 342
Check the hexadecimal conversion
1 × 16^2 + 5 × 16^1 + 6 × 16^0 = 342
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 342
- 342 squared
- 342 × 342 = 116,964
- 342 cubed
- 342 × 342 × 342 = 40,001,688
- Square root
- ≈ 18.493242
- Simplified radical
- 3√38
342 lies between 324 (18²) and 361 (19²), so it is not a perfect square. It is not a perfect cube.
342 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 342.
Distinguish a square from a square rootMultiplication table for 342
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 | 171 | 0 | Yes |
| 3 | 114 | 0 | Yes |
| 4 | 85 | 2 | No |
| 5 | 68 | 2 | No |
| 6 | 57 | 0 | Yes |
| 7 | 48 | 6 | No |
| 8 | 42 | 6 | No |
| 9 | 38 | 0 | Yes |
| 10 | 34 | 2 | No |
| 11 | 31 | 1 | No |
| 12 | 28 | 6 | No |
For example, 342 = 7 × 48 + 6. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 342
342 contains 3 decimal digits. Its digit sum is 3 + 4 + 2 = 9.
- 342: 3 + 4 + 2 = 9
The digital root is 9. Reversing its digits gives 243; 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, 342/100 simplifies to 171/50 by dividing both terms by their greatest common divisor, 2. Its decimal value is 3.42. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 342 and 12 is 6. Their least common multiple is 684. The identity GCD × LCM = 342 × 12 = 4104 checks both results.
Work through GCF and LCMQuestions about 342
What are the factors of 342?
The positive factors are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342. There are 12 factors, including 1 and 342.
Is 342 a prime number?
No. 342 is composite: 2 × 3^2 × 19 = 342.
How do you write 342 in Roman numerals?
342 is CCCXLII in standard subtractive Roman numeral notation.
What is the binary representation of 342?
342 in decimal is 101010110 in base 2. Adding its active place values gives 256 + 64 + 16 + 4 + 2 = 342.
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 342
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 342 add to 9. 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.