The number 224
224 is a composite number with 12 divisors. Its prime factorisation is × 7. Divisors (12): 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 224: a Harshad number: divisible by its digit sum 8.
- 2
224 is composite. Its prime factorisation is
- 3
The divisors add up to 504; without 224 itself that is 280, so 224 is abundant (280 is more than 224). Euler's totient φ(224) = 96 numbers up to 224 share no factor with it.
- 4
The digits of 224 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 21 steps to reach 1.
LaTeX source of the formulas on this page
\[ 224 = 2^{5} \times 7 \]224 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 504 |
| Euler totient φ(n) | 96 |
| Square | 50176 |
| Cube | 11239424 |
| Square root | 14.966630 (= 4√14) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 21 |
| Scientific notation | 2.24 × |
224 in other forms
| Form | Value |
|---|---|
| In words | two hundred and twenty-four |
| Roman numerals | CCXXIV |
| Binary (base 2) | 11100000 |
| Octal (base 8) | 340 |
| Hexadecimal (base 16) | E0 |
| Base 3 | 22022 |
| As time | 224 seconds = 3 min 44 s |
Is 224 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (224 ÷ 2 = 112) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (224 ÷ 4 = 56) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (224 ÷ 7 = 32) | 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 (224 ÷ 8 = 28) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 224 a prime number?
No. 224 = × 7, so it is divisible by 2.
What are the factors of 224?
1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224.
What is 224 in binary?
11100000 (hexadecimal E0, octal 340).
What is the square root of 224?
About 14.9666, exactly 4√14.
What is 224 in Roman numerals?
CCXXIV.
Is 224 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 224?
224 is a Harshad number: divisible by its digit sum 8.