The number 10200
10200 is a composite number with 48 divisors. Its prime factorisation is × 3 × × 17. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 25, 30, 34 … 10200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10200: a Harshad number: divisible by its digit sum 3.
- 2
10200 is composite. Its prime factorisation is
- 3
The divisors add up to 33480; without 10200 itself that is 23280, so 10200 is abundant (23280 is more than 10200). Euler's totient φ(10200) = 2560 numbers up to 10200 share no factor with it.
- 4
The digits of 10200 add up to 3, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 86 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10200 = 2^{3} \times 3 \times 5^{2} \times 17 \]10200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 33480 |
| Euler totient φ(n) | 2560 |
| Square | 104040000 |
| Cube | 1061208000000 |
| Square root | 100.995049 (= 10√102) |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 86 |
| Scientific notation | 1.02 × |
10200 in other forms
| Form | Value |
|---|---|
| In words | ten thousand two hundred |
| Binary (base 2) | 10011111011000 |
| Octal (base 8) | 23730 |
| Hexadecimal (base 16) | 27D8 |
| Base 3 | 111222210 |
| As time | 10200 seconds = 2 h 50 min 0 s |
Is 10200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10200 ÷ 2 = 5100) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10200 ÷ 3 = 3400) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10200 ÷ 4 = 2550) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10200 ÷ 5 = 2040) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (10200 ÷ 6 = 1700) | 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 (10200 ÷ 8 = 1275) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (10200 ÷ 10 = 1020) | 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 (10200 ÷ 12 = 850) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10200 a prime number?
No. 10200 = × 3 × × 17, so it is divisible by 2.
What are the factors of 10200?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 25, 30, 34, 40, 50, 51, 60, 68, 75, 85, 100, 102, 120, 136, 150, 170, 200, 204, 255, 300, 340, 408, 425, 510, 600, 680, 850, 1020, 1275, 1700, 2040, 2550, 3400, 5100, 10200.
What is 10200 in binary?
10011111011000 (hexadecimal 27D8, octal 23730).
What is the square root of 10200?
About 100.9950, exactly 10√102.
Is 10200 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 10200?
10200 is a Harshad number: divisible by its digit sum 3.