Number dictionary · Exact arithmetic
350: factors and number facts
three hundred fifty 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 fifty
- Roman numeral
- CCCL
- Prime factorization
- 2 × 5^2 × 7
- Digital root
- 8
All factors of 350
A positive factor divides 350 with no remainder. In ascending order, the complete list is:
1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350
Factor pairs
- 1 × 350 = 350
- 2 × 175 = 350
- 5 × 70 = 350
- 7 × 50 = 350
- 10 × 35 = 350
- 14 × 25 = 350
Each pair describes an arrangement of 350 items into equal rows. The pairs have different row and column counts; 350 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 12
- Sum of all divisors
- 744
- Sum excluding 350
- 394
- Classification
- abundant
350 is abundant because its proper divisors add to 394, which is greater than 350.
Prime factorization of 350
350 = 2 × 5^2 × 7
Repeated division, step by step
- 350 ÷ 2 = 175
- 175 ÷ 5 = 35
- 35 ÷ 5 = 7
- 7 ÷ 7 = 1
Multiply the prime divisors in these steps to reconstruct 350. 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 349. The next larger prime is 353. The factor list above explains why 350 is composite.
Learn the factorization method350 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred fifty |
| Roman numeral | CCCL |
| Binary (base 2) | 101011110 |
| Octal (base 8) | 536 |
| Decimal (base 10) | 350 |
| Hexadecimal (base 16) | 15E |
Check the binary conversion
Read 101011110 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 + 8 + 4 + 2 = 350
Check the hexadecimal conversion
1 × 16^2 + 5 × 16^1 + 14 × 16^0 = 350
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 350
- 350 squared
- 350 × 350 = 122,500
- 350 cubed
- 350 × 350 × 350 = 42,875,000
- Square root
- ≈ 18.708287
- Simplified radical
- 5√14
350 lies between 324 (18²) and 361 (19²), so it is not a perfect square. It is not a perfect cube.
350 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 350.
Distinguish a square from a square rootMultiplication table for 350
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 | 175 | 0 | Yes |
| 3 | 116 | 2 | No |
| 4 | 87 | 2 | No |
| 5 | 70 | 0 | Yes |
| 6 | 58 | 2 | No |
| 7 | 50 | 0 | Yes |
| 8 | 43 | 6 | No |
| 9 | 38 | 8 | No |
| 10 | 35 | 0 | Yes |
| 11 | 31 | 9 | No |
| 12 | 29 | 2 | No |
For example, 350 = 7 × 50 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 350
350 contains 3 decimal digits. Its digit sum is 3 + 5 + 0 = 8.
- 350: 3 + 5 + 0 = 8
The digital root is 8. Reversing its digits gives 053; 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, 350/100 simplifies to 7/2 by dividing both terms by their greatest common divisor, 50. Its decimal value is 3.5. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 350 and 12 is 2. Their least common multiple is 2100. The identity GCD × LCM = 350 × 12 = 4200 checks both results.
Work through GCF and LCMQuestions about 350
What are the factors of 350?
The positive factors are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350. There are 12 factors, including 1 and 350.
Is 350 a prime number?
No. 350 is composite: 2 × 5^2 × 7 = 350.
How do you write 350 in Roman numerals?
350 is CCCL in standard subtractive Roman numeral notation.
What is the binary representation of 350?
350 in decimal is 101011110 in base 2. Adding its active place values gives 256 + 64 + 16 + 8 + 4 + 2 = 350.
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 350
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 350 add to 8. 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.