Number dictionary · Exact arithmetic
352: factors and number facts
three hundred fifty-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 fifty-two
- Roman numeral
- CCCLII
- Prime factorization
- 2^5 × 11
- Digital root
- 1
All factors of 352
A positive factor divides 352 with no remainder. In ascending order, the complete list is:
1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352
Factor pairs
- 1 × 352 = 352
- 2 × 176 = 352
- 4 × 88 = 352
- 8 × 44 = 352
- 11 × 32 = 352
- 16 × 22 = 352
Each pair describes an arrangement of 352 items into equal rows. The pairs have different row and column counts; 352 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 12
- Sum of all divisors
- 756
- Sum excluding 352
- 404
- Classification
- abundant
352 is abundant because its proper divisors add to 404, which is greater than 352.
Prime factorization of 352
352 = 2^5 × 11
Repeated division, step by step
- 352 ÷ 2 = 176
- 176 ÷ 2 = 88
- 88 ÷ 2 = 44
- 44 ÷ 2 = 22
- 22 ÷ 2 = 11
- 11 ÷ 11 = 1
Multiply the prime divisors in these steps to reconstruct 352. An exponent records how many times the same prime occurs. The divisor-count calculation is (5 + 1) × (1 + 1) = 12.
The preceding prime is 349. The next larger prime is 353. The factor list above explains why 352 is composite.
Learn the factorization method352 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred fifty-two |
| Roman numeral | CCCLII |
| Binary (base 2) | 101100000 |
| Octal (base 8) | 540 |
| Decimal (base 10) | 352 |
| Hexadecimal (base 16) | 160 |
Check the binary conversion
Read 101100000 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 = 352
Check the hexadecimal conversion
1 × 16^2 + 6 × 16^1 + 0 × 16^0 = 352
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 352
- 352 squared
- 352 × 352 = 123,904
- 352 cubed
- 352 × 352 × 352 = 43,614,208
- Square root
- ≈ 18.761663
- Simplified radical
- 4√22
352 lies between 324 (18²) and 361 (19²), so it is not a perfect square. It is not a perfect cube.
352 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 352.
Distinguish a square from a square rootMultiplication table for 352
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 | 176 | 0 | Yes |
| 3 | 117 | 1 | No |
| 4 | 88 | 0 | Yes |
| 5 | 70 | 2 | No |
| 6 | 58 | 4 | No |
| 7 | 50 | 2 | No |
| 8 | 44 | 0 | Yes |
| 9 | 39 | 1 | No |
| 10 | 35 | 2 | No |
| 11 | 32 | 0 | Yes |
| 12 | 29 | 4 | No |
For example, 352 = 7 × 50 + 2. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 352
352 contains 3 decimal digits. Its digit sum is 3 + 5 + 2 = 10.
- 352: 3 + 5 + 2 = 10
- 10: 1 + 0 = 1
The digital root is 1. Reversing its digits gives 253; 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, 352/100 simplifies to 88/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 3.52. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 352 and 12 is 4. Their least common multiple is 1056. The identity GCD × LCM = 352 × 12 = 4224 checks both results.
Work through GCF and LCMQuestions about 352
What are the factors of 352?
The positive factors are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352. There are 12 factors, including 1 and 352.
Is 352 a prime number?
No. 352 is composite: 2^5 × 11 = 352.
How do you write 352 in Roman numerals?
352 is CCCLII in standard subtractive Roman numeral notation.
What is the binary representation of 352?
352 in decimal is 101100000 in base 2. Adding its active place values gives 256 + 64 + 32 = 352.
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 352
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 352 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.