The number 73800
73800 is a composite number with 72 divisors. Its prime factorisation is × × × 41. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30 … 73800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 73800: a Harshad number: divisible by its digit sum 18.
- 2
73800 is composite. Its prime factorisation is
- 3
The divisors add up to 253890; without 73800 itself that is 180090, so 73800 is abundant (180090 is more than 73800). Euler's totient φ(73800) = 19200 numbers up to 73800 share no factor with it.
- 4
The digits of 73800 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 231 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73800 = 2^{3} \times 3^{2} \times 5^{2} \times 41 \]73800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 253890 |
| Euler totient φ(n) | 19200 |
| Square | 5446440000 |
| Cube | 401947272000000 |
| Square root | 271.661554 (= 30√82) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 231 |
| Scientific notation | 7.38 × |
73800 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand eight hundred |
| Binary (base 2) | 10010000001001000 |
| Octal (base 8) | 220110 |
| Hexadecimal (base 16) | 12048 |
| Base 3 | 10202020100 |
| As time | 73800 seconds = 20 h 30 min 0 s |
Is 73800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (73800 ÷ 2 = 36900) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (73800 ÷ 3 = 24600) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (73800 ÷ 4 = 18450) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (73800 ÷ 5 = 14760) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (73800 ÷ 6 = 12300) | 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 (73800 ÷ 8 = 9225) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (73800 ÷ 9 = 8200) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (73800 ÷ 10 = 7380) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (73800 ÷ 12 = 6150) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 73800 a prime number?
No. 73800 = × × × 41, so it is divisible by 2.
What are the factors of 73800?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 41, 45, 50, 60, 72, 75, 82, 90, 100, 120, 123, 150, 164, 180, 200, 205, 225, 246, 300, 328, 360, 369, 410, 450, 492, 600, 615, 738, 820, 900, 984, 1025, 1230, 1476, 1640, 1800, 1845, 2050, 2460, 2952, 3075, 3690, 4100, 4920, 6150, 7380, 8200, 9225, 12300, 14760, 18450, 24600, 36900, 73800.
What is 73800 in binary?
10010000001001000 (hexadecimal 12048, octal 220110).
What is the square root of 73800?
About 271.6616, exactly 30√82.
Is 73800 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 73800?
73800 is a Harshad number: divisible by its digit sum 18.