The number 83200
83200 is a composite number with 54 divisors. Its prime factorisation is × × 13. Divisors (54): 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 64 … 83200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 83200: a Harshad number: divisible by its digit sum 13.
- 2
83200 is composite. Its prime factorisation is
- 3
The divisors add up to 221774; without 83200 itself that is 138574, so 83200 is abundant (138574 is more than 83200). Euler's totient φ(83200) = 30720 numbers up to 83200 share no factor with it.
- 4
The digits of 83200 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83200 = 2^{8} \times 5^{2} \times 13 \]83200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 54 |
| Sum of divisors | 221774 |
| Euler totient φ(n) | 30720 |
| Square | 6922240000 |
| Cube | 575930368000000 |
| Square root | 288.444102 (= 80√13) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 32 |
| Scientific notation | 8.32 × |
83200 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand two hundred |
| Binary (base 2) | 10100010100000000 |
| Octal (base 8) | 242400 |
| Hexadecimal (base 16) | 14500 |
| Base 3 | 11020010111 |
| As time | 83200 seconds = 23 h 6 min 40 s |
Is 83200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83200 ÷ 2 = 41600) | 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 (83200 ÷ 4 = 20800) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (83200 ÷ 5 = 16640) | 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 5) | 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 (83200 ÷ 8 = 10400) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (83200 ÷ 10 = 8320) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | 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 83200 a prime number?
No. 83200 = × × 13, so it is divisible by 2.
What are the factors of 83200?
1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 64, 65, 80, 100, 104, 128, 130, 160, 200, 208, 256, 260, 320, 325, 400, 416, 520, 640, 650, 800, 832, 1040, 1280, 1300, 1600, 1664, 2080, 2600, 3200, 3328, 4160, 5200, 6400, 8320, 10400, 16640, 20800, 41600, 83200.
What is 83200 in binary?
10100010100000000 (hexadecimal 14500, octal 242400).
What is the square root of 83200?
About 288.4441, exactly 80√13.
Is 83200 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 83200?
83200 is a Harshad number: divisible by its digit sum 13.