Number dictionary · Exact arithmetic
336: factors and number facts
three hundred thirty-six is an even number and is composite. Its 20 positive divisors form 10 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- three hundred thirty-six
- Roman numeral
- CCCXXXVI
- Prime factorization
- 2^4 × 3 × 7
- Digital root
- 3
All factors of 336
A positive factor divides 336 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336
Factor pairs
- 1 × 336 = 336
- 2 × 168 = 336
- 3 × 112 = 336
- 4 × 84 = 336
- 6 × 56 = 336
- 7 × 48 = 336
- 8 × 42 = 336
- 12 × 28 = 336
- 14 × 24 = 336
- 16 × 21 = 336
Each pair describes an arrangement of 336 items into equal rows. The pairs have different row and column counts; 336 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 20
- Sum of all divisors
- 992
- Sum excluding 336
- 656
- Classification
- abundant
336 is abundant because its proper divisors add to 656, which is greater than 336.
Prime factorization of 336
336 = 2^4 × 3 × 7
Repeated division, step by step
- 336 ÷ 2 = 168
- 168 ÷ 2 = 84
- 84 ÷ 2 = 42
- 42 ÷ 2 = 21
- 21 ÷ 3 = 7
- 7 ÷ 7 = 1
Multiply the prime divisors in these steps to reconstruct 336. An exponent records how many times the same prime occurs. The divisor-count calculation is (4 + 1) × (1 + 1) × (1 + 1) = 20.
The preceding prime is 331. The next larger prime is 337. The factor list above explains why 336 is composite.
Learn the factorization method336 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred thirty-six |
| Roman numeral | CCCXXXVI |
| Binary (base 2) | 101010000 |
| Octal (base 8) | 520 |
| Decimal (base 10) | 336 |
| Hexadecimal (base 16) | 150 |
Check the binary conversion
Read 101010000 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 = 336
Check the hexadecimal conversion
1 × 16^2 + 5 × 16^1 + 0 × 16^0 = 336
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 336
- 336 squared
- 336 × 336 = 112,896
- 336 cubed
- 336 × 336 × 336 = 37,933,056
- Square root
- ≈ 18.330303
- Simplified radical
- 4√21
336 lies between 324 (18²) and 361 (19²), so it is not a perfect square. It is not a perfect cube.
336 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 336.
Distinguish a square from a square rootMultiplication table for 336
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 | 168 | 0 | Yes |
| 3 | 112 | 0 | Yes |
| 4 | 84 | 0 | Yes |
| 5 | 67 | 1 | No |
| 6 | 56 | 0 | Yes |
| 7 | 48 | 0 | Yes |
| 8 | 42 | 0 | Yes |
| 9 | 37 | 3 | No |
| 10 | 33 | 6 | No |
| 11 | 30 | 6 | No |
| 12 | 28 | 0 | Yes |
For example, 336 = 7 × 48 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 336
336 contains 3 decimal digits. Its digit sum is 3 + 3 + 6 = 12.
- 336: 3 + 3 + 6 = 12
- 12: 1 + 2 = 3
The digital root is 3. Reversing its digits gives 633; 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, 336/100 simplifies to 84/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 3.36. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 336 and 12 is 12. Their least common multiple is 336. The identity GCD × LCM = 336 × 12 = 4032 checks both results.
Work through GCF and LCMQuestions about 336
What are the factors of 336?
The positive factors are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336. There are 20 factors, including 1 and 336.
Is 336 a prime number?
No. 336 is composite: 2^4 × 3 × 7 = 336.
How do you write 336 in Roman numerals?
336 is CCCXXXVI in standard subtractive Roman numeral notation.
What is the binary representation of 336?
336 in decimal is 101010000 in base 2. Adding its active place values gives 256 + 64 + 16 = 336.
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 336
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 336 add to 12. 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.