Number dictionary · Exact arithmetic
1224: factors and number facts
one thousand two hundred twenty-four is an even number and is composite. Its 24 positive divisors form 12 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- one thousand two hundred twenty-four
- Roman numeral
- MCCXXIV
- Prime factorization
- 2^3 × 3^2 × 17
- Digital root
- 9
All factors of 1224
A positive factor divides 1224 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224
Factor pairs
- 1 × 1224 = 1224
- 2 × 612 = 1224
- 3 × 408 = 1224
- 4 × 306 = 1224
- 6 × 204 = 1224
- 8 × 153 = 1224
- 9 × 136 = 1224
- 12 × 102 = 1224
- 17 × 72 = 1224
- 18 × 68 = 1224
- 24 × 51 = 1224
- 34 × 36 = 1224
Each pair describes an arrangement of 1224 items into equal rows. The pairs have different row and column counts; 1224 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 24
- Sum of all divisors
- 3510
- Sum excluding 1224
- 2286
- Classification
- abundant
1224 is abundant because its proper divisors add to 2286, which is greater than 1224.
Prime factorization of 1224
1224 = 2^3 × 3^2 × 17
Repeated division, step by step
- 1224 ÷ 2 = 612
- 612 ÷ 2 = 306
- 306 ÷ 2 = 153
- 153 ÷ 3 = 51
- 51 ÷ 3 = 17
- 17 ÷ 17 = 1
Multiply the prime divisors in these steps to reconstruct 1224. An exponent records how many times the same prime occurs. The divisor-count calculation is (3 + 1) × (2 + 1) × (1 + 1) = 24.
The preceding prime is 1223. The next larger prime is 1229. The factor list above explains why 1224 is composite.
Learn the factorization method1224 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one thousand two hundred twenty-four |
| Roman numeral | MCCXXIV |
| Binary (base 2) | 10011001000 |
| Octal (base 8) | 2310 |
| Decimal (base 10) | 1224 |
| Hexadecimal (base 16) | 4C8 |
Check the binary conversion
Read 10011001000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
1024 + 128 + 64 + 8 = 1224
Check the hexadecimal conversion
4 × 16^2 + 12 × 16^1 + 8 × 16^0 = 1224
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 1224
- 1224 squared
- 1224 × 1224 = 1,498,176
- 1224 cubed
- 1224 × 1224 × 1224 = 1,833,767,424
- Square root
- ≈ 34.985711
- Simplified radical
- 6√34
1224 lies between 1156 (34²) and 1225 (35²), so it is not a perfect square. It is not a perfect cube.
1224 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 1224.
Distinguish a square from a square rootMultiplication table for 1224
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 | 612 | 0 | Yes |
| 3 | 408 | 0 | Yes |
| 4 | 306 | 0 | Yes |
| 5 | 244 | 4 | No |
| 6 | 204 | 0 | Yes |
| 7 | 174 | 6 | No |
| 8 | 153 | 0 | Yes |
| 9 | 136 | 0 | Yes |
| 10 | 122 | 4 | No |
| 11 | 111 | 3 | No |
| 12 | 102 | 0 | Yes |
For example, 1224 = 7 × 174 + 6. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 1224
1224 contains 4 decimal digits. Its digit sum is 1 + 2 + 2 + 4 = 9.
- 1224: 1 + 2 + 2 + 4 = 9
The digital root is 9. Reversing its digits gives 4221; 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, 1224/100 simplifies to 306/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 12.24. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 1224 and 12 is 12. Their least common multiple is 1224. The identity GCD × LCM = 1224 × 12 = 14688 checks both results.
Work through GCF and LCMQuestions about 1224
What are the factors of 1224?
The positive factors are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224. There are 24 factors, including 1 and 1224.
Is 1224 a prime number?
No. 1224 is composite: 2^3 × 3^2 × 17 = 1224.
How do you write 1224 in Roman numerals?
1224 is MCCXXIV in standard subtractive Roman numeral notation.
What is the binary representation of 1224?
1224 in decimal is 10011001000 in base 2. Adding its active place values gives 1024 + 128 + 64 + 8 = 1224.
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 1224
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 1224 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.