The number 3200
3200 is a composite number with 24 divisors. Its prime factorisation is × . Divisors (24): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128 … 3200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3200: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 5.
- 2
3200 is composite. Its prime factorisation is
- 3
The divisors add up to 7905; without 3200 itself that is 4705, so 3200 is abundant (4705 is more than 3200). Euler's totient φ(3200) = 1280 numbers up to 3200 share no factor with it.
- 4
The digits of 3200 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 30 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3200 = 2^{7} \times 5^{2} \]3200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 7905 |
| Euler totient φ(n) | 1280 |
| Square | 10240000 |
| Cube | 32768000000 |
| Square root | 56.568542 (= 40√2) |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 30 |
| Scientific notation | 3.2 × |
3200 in other forms
| Form | Value |
|---|---|
| In words | three thousand two hundred |
| Roman numerals | MMMCC |
| Binary (base 2) | 110010000000 |
| Octal (base 8) | 6200 |
| Hexadecimal (base 16) | C80 |
| Base 3 | 11101112 |
| As time | 3200 seconds = 53 min 20 s |
Is 3200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3200 ÷ 2 = 1600) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3200 ÷ 4 = 800) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (3200 ÷ 5 = 640) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (3200 ÷ 8 = 400) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (3200 ÷ 10 = 320) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3200 a prime number?
No. 3200 = × , so it is divisible by 2.
What are the factors of 3200?
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 320, 400, 640, 800, 1600, 3200.
What is 3200 in binary?
110010000000 (hexadecimal C80, octal 6200).
What is the square root of 3200?
About 56.5685, exactly 40√2.
What is 3200 in Roman numerals?
MMMCC.
Is 3200 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 3200?
3200 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 5.