The number 73200
73200 is a composite number with 60 divisors. Its prime factorisation is × 3 × × 61. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40 … 73200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 73200: a Harshad number: divisible by its digit sum 12.
- 2
73200 is composite. Its prime factorisation is
- 3
The divisors add up to 238328; without 73200 itself that is 165128, so 73200 is abundant (165128 is more than 73200). Euler's totient φ(73200) = 19200 numbers up to 73200 share no factor with it.
- 4
The digits of 73200 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73200 = 2^{4} \times 3 \times 5^{2} \times 61 \]73200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 238328 |
| Euler totient φ(n) | 19200 |
| Square | 5358240000 |
| Cube | 392223168000000 |
| Square root | 270.554985 (= 20√183) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.32 × |
73200 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand two hundred |
| Binary (base 2) | 10001110111110000 |
| Octal (base 8) | 216760 |
| Hexadecimal (base 16) | 11DF0 |
| Base 3 | 10201102010 |
| As time | 73200 seconds = 20 h 20 min 0 s |
Is 73200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (73200 ÷ 2 = 36600) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (73200 ÷ 3 = 24400) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (73200 ÷ 4 = 18300) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (73200 ÷ 5 = 14640) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (73200 ÷ 6 = 12200) | 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 (73200 ÷ 8 = 9150) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (73200 ÷ 10 = 7320) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (73200 ÷ 12 = 6100) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 73200 a prime number?
No. 73200 = × 3 × × 61, so it is divisible by 2.
What are the factors of 73200?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 61, 75, 80, 100, 120, 122, 150, 183, 200, 240, 244, 300, 305, 366, 400, 488, 600, 610, 732, 915, 976, 1200, 1220, 1464, 1525, 1830, 2440, 2928, 3050, 3660, 4575, 4880, 6100, 7320, 9150, 12200, 14640, 18300, 24400, 36600, 73200.
What is 73200 in binary?
10001110111110000 (hexadecimal 11DF0, octal 216760).
What is the square root of 73200?
About 270.5550, exactly 20√183.
Is 73200 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 73200?
73200 is a Harshad number: divisible by its digit sum 12.