If a number is exactly divisible by both 11 and 13, it must also be divisible by their product, which is 143. This is because 11 and 13 are prime numbers.
Divisibility Rule Explained
The provided reference states that since 11 and 13 are prime numbers, any number divisible by both must also be divisible by their product (11 * 13 = 143).
Here's a more detailed look:
- Prime Numbers: Prime numbers are only divisible by 1 and themselves. Both 11 and 13 fit this definition.
- Divisibility: If a number is divisible by a prime number, it means that prime number is a factor of the original number.
- Combined Divisibility: When a number is divisible by two different prime numbers, like 11 and 13, it indicates that both 11 and 13 are factors. This also means the product of these factors (11 * 13) must also be a factor.
Practical Examples
Here are a few examples to illustrate the point:
| Number | Divisible by 11? | Divisible by 13? | Divisible by 143? |
|---|---|---|---|
| 143 | Yes | Yes | Yes |
| 286 | Yes | Yes | Yes |
| 429 | Yes | Yes | Yes |
| 150 | No | No | No |
| 585 | No | Yes | No |
| 363 | Yes | No | No |
As you can see, every number divisible by both 11 and 13 is also divisible by 143.
Key Takeaway
- If a number is divisible by 11 and 13, it is necessarily divisible by 143 (11 * 13).
