The number 72324
72324 is a composite number with 54 divisors. Its prime factorisation is × × × 41. Divisors (54): 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 41, 42, 49 … 72324.
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How to work it out
- 1
What is special about 72324: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
72324 is composite. Its prime factorisation is
- 3
The divisors add up to 217854; without 72324 itself that is 145530, so 72324 is abundant (145530 is more than 72324). Euler's totient φ(72324) = 20160 numbers up to 72324 share no factor with it.
- 4
The digits of 72324 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 94 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72324 = 2^{2} \times 3^{2} \times 7^{2} \times 41 \]72324 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 54 |
| Sum of divisors | 217854 |
| Euler totient φ(n) | 20160 |
| Square | 5230760976 |
| Cube | 378309556828224 |
| Square root | 268.931218 (= 42√41) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 94 |
| Scientific notation | 7.2324 × |
72324 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand three hundred and twenty-four |
| Binary (base 2) | 10001101010000100 |
| Octal (base 8) | 215204 |
| Hexadecimal (base 16) | 11A84 |
| Base 3 | 10200012200 |
| As time | 72324 seconds = 20 h 5 min 24 s |
Is 72324 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72324 ÷ 2 = 36162) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72324 ÷ 3 = 24108) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72324 ÷ 4 = 18081) | 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 (72324 ÷ 6 = 12054) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (72324 ÷ 7 = 10332) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (72324 ÷ 9 = 8036) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72324 ÷ 12 = 6027) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72324 a prime number?
No. 72324 = × × × 41, so it is divisible by 2.
What are the factors of 72324?
1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 41, 42, 49, 63, 82, 84, 98, 123, 126, 147, 164, 196, 246, 252, 287, 294, 369, 441, 492, 574, 588, 738, 861, 882, 1148, 1476, 1722, 1764, 2009, 2583, 3444, 4018, 5166, 6027, 8036, 10332, 12054, 18081, 24108, 36162, 72324.
What is 72324 in binary?
10001101010000100 (hexadecimal 11A84, octal 215204).
What is the square root of 72324?
About 268.9312, exactly 42√41.
Is 72324 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 72324?
72324 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.