The number 30024
30024 is a composite number with 32 divisors. Its prime factorisation is × × 139. Divisors (32): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 139 … 30024.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 30024: a Harshad number: divisible by its digit sum 9.
- 2
30024 is composite. Its prime factorisation is
- 3
The divisors add up to 84000; without 30024 itself that is 53976, so 30024 is abundant (53976 is more than 30024). Euler's totient φ(30024) = 9936 numbers up to 30024 share no factor with it.
- 4
The digits of 30024 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 165 steps to reach 1.
LaTeX source of the formulas on this page
\[ 30024 = 2^{3} \times 3^{3} \times 139 \]30024 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 84000 |
| Euler totient φ(n) | 9936 |
| Square | 901440576 |
| Cube | 27064851853824 |
| Square root | 173.274349 (= 6√834) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 165 |
| Scientific notation | 3.0024 × |
30024 in other forms
| Form | Value |
|---|---|
| In words | thirty thousand and twenty-four |
| Binary (base 2) | 111010101001000 |
| Octal (base 8) | 72510 |
| Hexadecimal (base 16) | 7548 |
| Base 3 | 1112012000 |
| As time | 30024 seconds = 8 h 20 min 24 s |
Is 30024 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (30024 ÷ 2 = 15012) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (30024 ÷ 3 = 10008) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (30024 ÷ 4 = 7506) | 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 (30024 ÷ 6 = 5004) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (30024 ÷ 8 = 3753) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (30024 ÷ 9 = 3336) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (30024 ÷ 12 = 2502) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 30024 a prime number?
No. 30024 = × × 139, so it is divisible by 2.
What are the factors of 30024?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 139, 216, 278, 417, 556, 834, 1112, 1251, 1668, 2502, 3336, 3753, 5004, 7506, 10008, 15012, 30024.
What is 30024 in binary?
111010101001000 (hexadecimal 7548, octal 72510).
What is the square root of 30024?
About 173.2743, exactly 6√834.
Is 30024 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 30024?
30024 is a Harshad number: divisible by its digit sum 9.