The number 23200
23200 is a composite number with 36 divisors. Its prime factorisation is × × 29. Divisors (36): 1, 2, 4, 5, 8, 10, 16, 20, 25, 29, 32, 40, 50, 58, 80, 100 … 23200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
23200 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
23200 is composite. Its prime factorisation is
- 3
The divisors add up to 58590; without 23200 itself that is 35390, so 23200 is abundant (35390 is more than 23200). Euler's totient φ(23200) = 8960 numbers up to 23200 share no factor with it.
- 4
The digits of 23200 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 25 steps to reach 1.
LaTeX source of the formulas on this page
\[ 23200 = 2^{5} \times 5^{2} \times 29 \]23200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 58590 |
| Euler totient φ(n) | 8960 |
| Square | 538240000 |
| Cube | 12487168000000 |
| Square root | 152.315462 (= 20√58) |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 25 |
| Scientific notation | 2.32 × |
23200 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand two hundred |
| Binary (base 2) | 101101010100000 |
| Octal (base 8) | 55240 |
| Hexadecimal (base 16) | 5AA0 |
| Base 3 | 1011211021 |
| As time | 23200 seconds = 6 h 26 min 40 s |
Is 23200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (23200 ÷ 2 = 11600) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (23200 ÷ 4 = 5800) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (23200 ÷ 5 = 4640) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (23200 ÷ 8 = 2900) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (23200 ÷ 10 = 2320) | 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 23200 a prime number?
No. 23200 = × × 29, so it is divisible by 2.
What are the factors of 23200?
1, 2, 4, 5, 8, 10, 16, 20, 25, 29, 32, 40, 50, 58, 80, 100, 116, 145, 160, 200, 232, 290, 400, 464, 580, 725, 800, 928, 1160, 1450, 2320, 2900, 4640, 5800, 11600, 23200.
What is 23200 in binary?
101101010100000 (hexadecimal 5AA0, octal 55240).
What is the square root of 23200?
About 152.3155, exactly 20√58.
Is 23200 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 23200?
It is a composite number with 36 divisors.