Yes, all numbers divisible by 6 are also divisible by 3.
The divisibility rule for 6 states that a number is divisible by 6 if it is divisible by both 2 and 3. This is because 6 can be factored into 2 multiplied by 3 (6 = 2 * 3).
Explanation
Let's break it down:
- Divisibility by 6 means a number can be divided by 6 with no remainder.
- Since 6 = 2 * 3, any number that's divisible by 6 must also be divisible by both 2 and 3.
- The reference states: "6 = 2\*3, so **any number divisible by 6 must be divisible by both 2 and 3, hence must be divisible by 3**."
Examples
Here are a few examples:
| Number | Divisible by 6? | Divisible by 3? |
|---|---|---|
| 6 | Yes (6 / 6 = 1) | Yes (6 / 3 = 2) |
| 12 | Yes (12 / 6 = 2) | Yes (12 / 3 = 4) |
| 18 | Yes (18 / 6 = 3) | Yes (18 / 3 = 6) |
| 30 | Yes (30 / 6 = 5) | Yes (30 / 3 = 10) |
| 27 | No | Yes (27 / 3 = 9) |
Notice that all numbers divisible by 6 (6, 12, 18, 30) are also divisible by 3.
It's also important to remember the converse is not true. A number divisible by 3 is not *necessarily* divisible by 6 (see the example of 27). It must also be divisible by 2 to be divisible by 6.
