The number 43200
43200 is a composite number with 84 divisors. Its prime factorisation is × × . Divisors (84): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25 … 43200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 43200: a Harshad number: divisible by its digit sum 9.
- 2
43200 is composite. Its prime factorisation is
- 3
The divisors add up to 157480; without 43200 itself that is 114280, so 43200 is abundant (114280 is more than 43200). Euler's totient φ(43200) = 11520 numbers up to 43200 share no factor with it.
- 4
The digits of 43200 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 119 steps to reach 1.
LaTeX source of the formulas on this page
\[ 43200 = 2^{6} \times 3^{3} \times 5^{2} \]43200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 84 |
| Sum of divisors | 157480 |
| Euler totient φ(n) | 11520 |
| Square | 1866240000 |
| Cube | 80621568000000 |
| Square root | 207.846097 (= 120√3) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 119 |
| Scientific notation | 4.32 × |
43200 in other forms
| Form | Value |
|---|---|
| In words | forty-three thousand two hundred |
| Binary (base 2) | 1010100011000000 |
| Octal (base 8) | 124300 |
| Hexadecimal (base 16) | A8C0 |
| Base 3 | 2012021000 |
| As time | 43200 seconds = 12 h 0 min 0 s |
Is 43200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (43200 ÷ 2 = 21600) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (43200 ÷ 3 = 14400) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (43200 ÷ 4 = 10800) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (43200 ÷ 5 = 8640) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (43200 ÷ 6 = 7200) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (43200 ÷ 8 = 5400) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (43200 ÷ 9 = 4800) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (43200 ÷ 10 = 4320) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (43200 ÷ 12 = 3600) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 43200 a prime number?
No. 43200 = × × , so it is divisible by 2.
What are the factors of 43200?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 192, 200, 216, 225, 240, 270, 288, 300, 320, 360, 400, 432, 450, 480, 540, 576, 600, 675, 720, 800, 864, 900, 960, 1080, 1200, 1350, 1440, 1600, 1728, 1800, 2160, 2400, 2700, 2880, 3600, 4320, 4800, 5400, 7200, 8640, 10800, 14400, 21600, 43200.
What is 43200 in binary?
1010100011000000 (hexadecimal A8C0, octal 124300).
What is the square root of 43200?
About 207.8461, exactly 120√3.
Is 43200 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 43200?
43200 is a Harshad number: divisible by its digit sum 9.