The number 75024
75024 is a composite number with 30 divisors. Its prime factorisation is × × 521. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 521 … 75024.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 75024: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
75024 is composite. Its prime factorisation is
- 3
The divisors add up to 210366; without 75024 itself that is 135342, so 75024 is abundant (135342 is more than 75024). Euler's totient φ(75024) = 24960 numbers up to 75024 share no factor with it.
- 4
The digits of 75024 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
\[ 75024 = 2^{4} \times 3^{2} \times 521 \]75024 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 210366 |
| Euler totient φ(n) | 24960 |
| Square | 5628600576 |
| Cube | 422280129613824 |
| Square root | 273.905093 (= 12√521) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 156 |
| Scientific notation | 7.5024 × |
75024 in other forms
| Form | Value |
|---|---|
| In words | seventy-five thousand and twenty-four |
| Binary (base 2) | 10010010100010000 |
| Octal (base 8) | 222420 |
| Hexadecimal (base 16) | 12510 |
| Base 3 | 10210220200 |
| As time | 75024 seconds = 20 h 50 min 24 s |
Is 75024 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (75024 ÷ 2 = 37512) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (75024 ÷ 3 = 25008) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (75024 ÷ 4 = 18756) | 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 (75024 ÷ 6 = 12504) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (75024 ÷ 8 = 9378) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (75024 ÷ 9 = 8336) | 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 | Yes (75024 ÷ 12 = 6252) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 75024 a prime number?
No. 75024 = × × 521, so it is divisible by 2.
What are the factors of 75024?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 521, 1042, 1563, 2084, 3126, 4168, 4689, 6252, 8336, 9378, 12504, 18756, 25008, 37512, 75024.
What is 75024 in binary?
10010010100010000 (hexadecimal 12510, octal 222420).
What is the square root of 75024?
About 273.9051, exactly 12√521.
Is 75024 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 75024?
75024 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.