The number 67224
67224 is a composite number with 16 divisors. Its prime factorisation is × 3 × 2801. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 2801, 5602, 8403, 11204, 16806, 22408, 33612, 67224.
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How to work it out
- 1
What is special about 67224: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
67224 is composite. Its prime factorisation is
- 3
The divisors add up to 168120; without 67224 itself that is 100896, so 67224 is abundant (100896 is more than 67224). Euler's totient φ(67224) = 22400 numbers up to 67224 share no factor with it.
- 4
The digits of 67224 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 67224 = 2^{3} \times 3 \times 2801 \]67224 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 168120 |
| Euler totient φ(n) | 22400 |
| Square | 4519066176 |
| Cube | 303789704615424 |
| Square root | 259.275915 (= 2√16806) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 68 |
| Scientific notation | 6.7224 × |
67224 in other forms
| Form | Value |
|---|---|
| In words | sixty-seven thousand two hundred and twenty-four |
| Binary (base 2) | 10000011010011000 |
| Octal (base 8) | 203230 |
| Hexadecimal (base 16) | 10698 |
| Base 3 | 10102012210 |
| As time | 67224 seconds = 18 h 40 min 24 s |
Is 67224 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (67224 ÷ 2 = 33612) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (67224 ÷ 3 = 22408) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (67224 ÷ 4 = 16806) | 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 (67224 ÷ 6 = 11204) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (67224 ÷ 8 = 8403) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 (67224 ÷ 12 = 5602) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 67224 a prime number?
No. 67224 = × 3 × 2801, so it is divisible by 2.
What are the factors of 67224?
1, 2, 3, 4, 6, 8, 12, 24, 2801, 5602, 8403, 11204, 16806, 22408, 33612, 67224.
What is 67224 in binary?
10000011010011000 (hexadecimal 10698, octal 203230).
What is the square root of 67224?
About 259.2759, exactly 2√16806.
Is 67224 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 67224?
67224 is a happy number: repeatedly adding the squares of its digits reaches 1.