The number 1224
1224 is a composite number with 24 divisors. Its prime factorisation is × × 17. Divisors (24): 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72 … 1224.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1224: a Harshad number: divisible by its digit sum 9.
- 2
1224 is composite. Its prime factorisation is
- 3
The divisors add up to 3510; without 1224 itself that is 2286, so 1224 is abundant (2286 is more than 1224). Euler's totient φ(1224) = 384 numbers up to 1224 share no factor with it.
- 4
The digits of 1224 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1224 = 2^{3} \times 3^{2} \times 17 \]1224 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 3510 |
| Euler totient φ(n) | 384 |
| Square | 1498176 |
| Cube | 1833767424 |
| Square root | 34.985711 (= 6√34) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 39 |
| Scientific notation | 1.224 × |
1224 in other forms
| Form | Value |
|---|---|
| In words | one thousand two hundred and twenty-four |
| Roman numerals | MCCXXIV |
| Binary (base 2) | 10011001000 |
| Octal (base 8) | 2310 |
| Hexadecimal (base 16) | 4C8 |
| Base 3 | 1200100 |
| As time | 1224 seconds = 20 min 24 s |
Is 1224 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1224 ÷ 2 = 612) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1224 ÷ 3 = 408) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1224 ÷ 4 = 306) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1224 ÷ 6 = 204) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (1224 ÷ 8 = 153) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1224 ÷ 9 = 136) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1224 ÷ 12 = 102) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1224 a prime number?
No. 1224 = × × 17, so it is divisible by 2.
What are the factors of 1224?
1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224.
What is 1224 in binary?
10011001000 (hexadecimal 4C8, octal 2310).
What is the square root of 1224?
About 34.9857, exactly 6√34.
What is 1224 in Roman numerals?
MCCXXIV.
Is 1224 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1224?
1224 is a Harshad number: divisible by its digit sum 9.