Number dictionary · Exact arithmetic
216: factors and number facts
two hundred sixteen is an even number and is composite. Its 16 positive divisors form 8 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- two hundred sixteen
- Roman numeral
- CCXVI
- Prime factorization
- 2^3 × 3^3
- Digital root
- 9
All factors of 216
A positive factor divides 216 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
Factor pairs
- 1 × 216 = 216
- 2 × 108 = 216
- 3 × 72 = 216
- 4 × 54 = 216
- 6 × 36 = 216
- 8 × 27 = 216
- 9 × 24 = 216
- 12 × 18 = 216
Each pair describes an arrangement of 216 items into equal rows. The pairs have different row and column counts; 216 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 16
- Sum of all divisors
- 600
- Sum excluding 216
- 384
- Classification
- abundant
216 is abundant because its proper divisors add to 384, which is greater than 216.
Prime factorization of 216
216 = 2^3 × 3^3
Repeated division, step by step
- 216 ÷ 2 = 108
- 108 ÷ 2 = 54
- 54 ÷ 2 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1
Multiply the prime divisors in these steps to reconstruct 216. An exponent records how many times the same prime occurs. The divisor-count calculation is (3 + 1) × (3 + 1) = 16.
The preceding prime is 211. The next larger prime is 223. The factor list above explains why 216 is composite.
Learn the factorization method216 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | two hundred sixteen |
| Roman numeral | CCXVI |
| Binary (base 2) | 11011000 |
| Octal (base 8) | 330 |
| Decimal (base 10) | 216 |
| Hexadecimal (base 16) | D8 |
Check the binary conversion
Read 11011000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
128 + 64 + 16 + 8 = 216
Check the hexadecimal conversion
13 × 16^1 + 8 × 16^0 = 216
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 216
- 216 squared
- 216 × 216 = 46,656
- 216 cubed
- 216 × 216 × 216 = 10,077,696
- Square root
- ≈ 14.696938
- Simplified radical
- 6√6
216 lies between 196 (14²) and 225 (15²), so it is not a perfect square. It is also a perfect cube: 6³ = 216.
216 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 216.
Distinguish a square from a square rootMultiplication table for 216
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 | 108 | 0 | Yes |
| 3 | 72 | 0 | Yes |
| 4 | 54 | 0 | Yes |
| 5 | 43 | 1 | No |
| 6 | 36 | 0 | Yes |
| 7 | 30 | 6 | No |
| 8 | 27 | 0 | Yes |
| 9 | 24 | 0 | Yes |
| 10 | 21 | 6 | No |
| 11 | 19 | 7 | No |
| 12 | 18 | 0 | Yes |
For example, 216 = 7 × 30 + 6. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 216
216 contains 3 decimal digits. Its digit sum is 2 + 1 + 6 = 9.
- 216: 2 + 1 + 6 = 9
The digital root is 9. Reversing its digits gives 612; 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, 216/100 simplifies to 54/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 2.16. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 216 and 12 is 12. Their least common multiple is 216. The identity GCD × LCM = 216 × 12 = 2592 checks both results.
Work through GCF and LCMQuestions about 216
What are the factors of 216?
The positive factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216. There are 16 factors, including 1 and 216.
Is 216 a prime number?
No. 216 is composite: 2^3 × 3^3 = 216.
How do you write 216 in Roman numerals?
216 is CCXVI in standard subtractive Roman numeral notation.
What is the binary representation of 216?
216 in decimal is 11011000 in base 2. Adding its active place values gives 128 + 64 + 16 + 8 = 216.
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 216
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 216 add to 9. 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.