The number 75200
75200 is a composite number with 42 divisors. Its prime factorisation is × × 47. Divisors (42): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 47, 50, 64, 80, 94 … 75200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
75200 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
75200 is composite. Its prime factorisation is
- 3
The divisors add up to 188976; without 75200 itself that is 113776, so 75200 is abundant (113776 is more than 75200). Euler's totient φ(75200) = 29440 numbers up to 75200 share no factor with it.
- 4
The digits of 75200 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 75200 = 2^{6} \times 5^{2} \times 47 \]75200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 188976 |
| Euler totient φ(n) | 29440 |
| Square | 5655040000 |
| Cube | 425259008000000 |
| Square root | 274.226184 (= 40√47) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.52 × |
75200 in other forms
| Form | Value |
|---|---|
| In words | seventy-five thousand two hundred |
| Binary (base 2) | 10010010111000000 |
| Octal (base 8) | 222700 |
| Hexadecimal (base 16) | 125C0 |
| Base 3 | 10211011012 |
| As time | 75200 seconds = 20 h 53 min 20 s |
Is 75200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (75200 ÷ 2 = 37600) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (75200 ÷ 4 = 18800) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (75200 ÷ 5 = 15040) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (75200 ÷ 8 = 9400) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (75200 ÷ 10 = 7520) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 75200 a prime number?
No. 75200 = × × 47, so it is divisible by 2.
What are the factors of 75200?
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 47, 50, 64, 80, 94, 100, 160, 188, 200, 235, 320, 376, 400, 470, 752, 800, 940, 1175, 1504, 1600, 1880, 2350, 3008, 3760, 4700, 7520, 9400, 15040, 18800, 37600, 75200.
What is 75200 in binary?
10010010111000000 (hexadecimal 125C0, octal 222700).
What is the square root of 75200?
About 274.2262, exactly 40√47.
Is 75200 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 75200?
It is a composite number with 42 divisors.