Number dictionary · Exact arithmetic
343: factors and number facts
three hundred forty-three is an odd number and is composite. Its 4 positive divisors form 2 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- three hundred forty-three
- Roman numeral
- CCCXLIII
- Prime factorization
- 7^3
- Digital root
- 1
All factors of 343
A positive factor divides 343 with no remainder. In ascending order, the complete list is:
1, 7, 49, 343
Factor pairs
- 1 × 343 = 343
- 7 × 49 = 343
Each pair describes an arrangement of 343 items into equal rows. The pairs have different row and column counts; 343 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 4
- Sum of all divisors
- 400
- Sum excluding 343
- 57
- Classification
- deficient
343 is deficient because its proper divisors add to 57, which is less than 343.
Prime factorization of 343
343 = 7^3
Repeated division, step by step
- 343 ÷ 7 = 49
- 49 ÷ 7 = 7
- 7 ÷ 7 = 1
Multiply the prime divisors in these steps to reconstruct 343. An exponent records how many times the same prime occurs. The divisor-count calculation is (3 + 1) = 4.
The preceding prime is 337. The next larger prime is 347. The factor list above explains why 343 is composite.
Learn the factorization method343 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred forty-three |
| Roman numeral | CCCXLIII |
| Binary (base 2) | 101010111 |
| Octal (base 8) | 527 |
| Decimal (base 10) | 343 |
| Hexadecimal (base 16) | 157 |
Check the binary conversion
Read 101010111 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 + 1 = 343
Check the hexadecimal conversion
1 × 16^2 + 5 × 16^1 + 7 × 16^0 = 343
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 343
- 343 squared
- 343 × 343 = 117,649
- 343 cubed
- 343 × 343 × 343 = 40,353,607
- Square root
- ≈ 18.520259
- Simplified radical
- 7√7
343 lies between 324 (18²) and 361 (19²), so it is not a perfect square. It is also a perfect cube: 7³ = 343.
343 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 343.
Distinguish a square from a square rootMultiplication table for 343
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 | 1 | No |
| 3 | 114 | 1 | No |
| 4 | 85 | 3 | No |
| 5 | 68 | 3 | No |
| 6 | 57 | 1 | No |
| 7 | 49 | 0 | Yes |
| 8 | 42 | 7 | No |
| 9 | 38 | 1 | No |
| 10 | 34 | 3 | No |
| 11 | 31 | 2 | No |
| 12 | 28 | 7 | No |
For example, 343 = 7 × 49 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 343
343 contains 3 decimal digits. Its digit sum is 3 + 4 + 3 = 10.
- 343: 3 + 4 + 3 = 10
- 10: 1 + 0 = 1
The digital root is 1. 343 reads the same forward and backward, making it 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, 343/100 simplifies to 343/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 3.43. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 343 and 12 is 1. Their least common multiple is 4116. The identity GCD × LCM = 343 × 12 = 4116 checks both results.
Work through GCF and LCMQuestions about 343
What are the factors of 343?
The positive factors are 1, 7, 49, 343. There are 4 factors, including 1 and 343.
Is 343 a prime number?
No. 343 is composite: 7^3 = 343.
How do you write 343 in Roman numerals?
343 is CCCXLIII in standard subtractive Roman numeral notation.
What is the binary representation of 343?
343 in decimal is 101010111 in base 2. Adding its active place values gives 256 + 64 + 16 + 4 + 2 + 1 = 343.
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 343
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 343 add to 10. 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.