The number 73224
73224 is a composite number with 40 divisors. Its prime factorisation is × × 113. Divisors (40): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108 … 73224.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 73224: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
73224 is composite. Its prime factorisation is
- 3
The divisors add up to 206910; without 73224 itself that is 133686, so 73224 is abundant (133686 is more than 73224). Euler's totient φ(73224) = 24192 numbers up to 73224 share no factor with it.
- 4
The digits of 73224 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 156 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73224 = 2^{3} \times 3^{4} \times 113 \]73224 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 206910 |
| Euler totient φ(n) | 24192 |
| Square | 5361754176 |
| Cube | 392609087783424 |
| Square root | 270.599335 (= 18√226) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 156 |
| Scientific notation | 7.3224 × |
73224 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand two hundred and twenty-four |
| Binary (base 2) | 10001111000001000 |
| Octal (base 8) | 217010 |
| Hexadecimal (base 16) | 11E08 |
| Base 3 | 10201110000 |
| As time | 73224 seconds = 20 h 20 min 24 s |
Is 73224 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (73224 ÷ 2 = 36612) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (73224 ÷ 3 = 24408) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (73224 ÷ 4 = 18306) | 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 (73224 ÷ 6 = 12204) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (73224 ÷ 8 = 9153) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (73224 ÷ 9 = 8136) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (73224 ÷ 12 = 6102) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 73224 a prime number?
No. 73224 = × × 113, so it is divisible by 2.
What are the factors of 73224?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 113, 162, 216, 226, 324, 339, 452, 648, 678, 904, 1017, 1356, 2034, 2712, 3051, 4068, 6102, 8136, 9153, 12204, 18306, 24408, 36612, 73224.
What is 73224 in binary?
10001111000001000 (hexadecimal 11E08, octal 217010).
What is the square root of 73224?
About 270.5993, exactly 18√226.
Is 73224 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 73224?
73224 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.