The number 10209
10209 is a composite number with 8 divisors. Its prime factorisation is 3 × 41 × 83. Divisors (8): 1, 3, 41, 83, 123, 249, 3403, 10209.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10209: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
10209 is composite. Its prime factorisation is
- 3
The divisors add up to 14112; without 10209 itself that is 3903, so 10209 is deficient (3903 is less than 10209). Euler's totient φ(10209) = 6560 numbers up to 10209 share no factor with it.
- 4
The digits of 10209 add up to 12, 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
\[ 10209 = 3 \times 41 \times 83 \]
10209 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 14112 |
| Euler totient φ(n) | 6560 |
| Square | 104223681 |
| Cube | 1064019559329 |
| Square root | 101.039596 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 86 |
| Scientific notation | 1.0209 × |
10209 in other forms
| Form | Value |
|---|---|
| In words | ten thousand two hundred and nine |
| Binary (base 2) | 10011111100001 |
| Octal (base 8) | 23741 |
| Hexadecimal (base 16) | 27E1 |
| Base 3 | 112000010 |
| As time | 10209 seconds = 2 h 50 min 9 s |
Is 10209 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10209 ÷ 3 = 3403) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | No (remainder 1) | 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 | No (remainder 9) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10209 a prime number?
No. 10209 = 3 × 41 × 83, so it is divisible by 3.
What are the factors of 10209?
1, 3, 41, 83, 123, 249, 3403, 10209.
What is 10209 in binary?
10011111100001 (hexadecimal 27E1, octal 23741).
What is the square root of 10209?
About 101.0396.
Is 10209 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 10209?
10209 is a happy number: repeatedly adding the squares of its digits reaches 1.