The number 32400
32400 is a perfect square (180²). Its prime factorisation is × × . Divisors (75): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25 … 32400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32400: a perfect square (180²); a Harshad number: divisible by its digit sum 9.
- 2
32400 is composite. Its prime factorisation is
- 3
The divisors add up to 116281; without 32400 itself that is 83881, so 32400 is abundant (83881 is more than 32400). Euler's totient φ(32400) = 8640 numbers up to 32400 share no factor with it.
- 4
The digits of 32400 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 160 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32400 = 2^{4} \times 3^{4} \times 5^{2} \]32400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 75 |
| Sum of divisors | 116281 |
| Euler totient φ(n) | 8640 |
| Square | 1049760000 |
| Cube | 34012224000000 |
| Square root | 180 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 160 |
| Scientific notation | 3.24 × |
| Perfect power |
32400 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand four hundred |
| Binary (base 2) | 111111010010000 |
| Octal (base 8) | 77220 |
| Hexadecimal (base 16) | 7E90 |
| Base 3 | 1122110000 |
| As time | 32400 seconds = 9 h 0 min 0 s |
Is 32400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32400 ÷ 2 = 16200) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32400 ÷ 3 = 10800) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32400 ÷ 4 = 8100) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (32400 ÷ 5 = 6480) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (32400 ÷ 6 = 5400) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (32400 ÷ 8 = 4050) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (32400 ÷ 9 = 3600) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (32400 ÷ 10 = 3240) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (32400 ÷ 12 = 2700) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32400 a prime number?
No. 32400 = × × , so it is divisible by 2.
What are the factors of 32400?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200, 32400.
What is 32400 in binary?
111111010010000 (hexadecimal 7E90, octal 77220).
What is the square root of 32400?
180, because 180 × 180 = 32400.
Is 32400 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 32400?
32400 is a perfect square (180²); a Harshad number: divisible by its digit sum 9.