Number dictionary · Exact arithmetic
357: factors and number facts
three hundred fifty-seven is an odd number and is composite. Its 8 positive divisors form 4 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- three hundred fifty-seven
- Roman numeral
- CCCLVII
- Prime factorization
- 3 × 7 × 17
- Digital root
- 6
All factors of 357
A positive factor divides 357 with no remainder. In ascending order, the complete list is:
1, 3, 7, 17, 21, 51, 119, 357
Factor pairs
- 1 × 357 = 357
- 3 × 119 = 357
- 7 × 51 = 357
- 17 × 21 = 357
Each pair describes an arrangement of 357 items into equal rows. The pairs have different row and column counts; 357 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 8
- Sum of all divisors
- 576
- Sum excluding 357
- 219
- Classification
- deficient
357 is deficient because its proper divisors add to 219, which is less than 357.
Prime factorization of 357
357 = 3 × 7 × 17
Repeated division, step by step
- 357 ÷ 3 = 119
- 119 ÷ 7 = 17
- 17 ÷ 17 = 1
Multiply the prime divisors in these steps to reconstruct 357. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) × (1 + 1) = 8.
The preceding prime is 353. The next larger prime is 359. The factor list above explains why 357 is composite.
Learn the factorization method357 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred fifty-seven |
| Roman numeral | CCCLVII |
| Binary (base 2) | 101100101 |
| Octal (base 8) | 545 |
| Decimal (base 10) | 357 |
| Hexadecimal (base 16) | 165 |
Check the binary conversion
Read 101100101 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 + 32 + 4 + 1 = 357
Check the hexadecimal conversion
1 × 16^2 + 6 × 16^1 + 5 × 16^0 = 357
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 357
- 357 squared
- 357 × 357 = 127,449
- 357 cubed
- 357 × 357 × 357 = 45,499,293
- Square root
- ≈ 18.894444
- Simplified radical
- √357
357 lies between 324 (18²) and 361 (19²), so it is not a perfect square. It is not a perfect cube.
357 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 357.
Distinguish a square from a square rootMultiplication table for 357
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 | 178 | 1 | No |
| 3 | 119 | 0 | Yes |
| 4 | 89 | 1 | No |
| 5 | 71 | 2 | No |
| 6 | 59 | 3 | No |
| 7 | 51 | 0 | Yes |
| 8 | 44 | 5 | No |
| 9 | 39 | 6 | No |
| 10 | 35 | 7 | No |
| 11 | 32 | 5 | No |
| 12 | 29 | 9 | No |
For example, 357 = 7 × 51 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 357
357 contains 3 decimal digits. Its digit sum is 3 + 5 + 7 = 15.
- 357: 3 + 5 + 7 = 15
- 15: 1 + 5 = 6
The digital root is 6. Reversing its digits gives 753; 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, 357/100 simplifies to 357/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 3.57. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 357 and 12 is 3. Their least common multiple is 1428. The identity GCD × LCM = 357 × 12 = 4284 checks both results.
Work through GCF and LCMQuestions about 357
What are the factors of 357?
The positive factors are 1, 3, 7, 17, 21, 51, 119, 357. There are 8 factors, including 1 and 357.
Is 357 a prime number?
No. 357 is composite: 3 × 7 × 17 = 357.
How do you write 357 in Roman numerals?
357 is CCCLVII in standard subtractive Roman numeral notation.
What is the binary representation of 357?
357 in decimal is 101100101 in base 2. Adding its active place values gives 256 + 64 + 32 + 4 + 1 = 357.
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 357
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 357 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.