Divisibility Rules: Is Every Multiple of 2 Also Divisible by 6?

Will a number divisible by 2 necessarily be divisible by 6?

To determine if a number divisible by 2 is also divisible by 6, we need to understand the rules of divisibility:

• A number is divisible by 2 if it is an even number, i.e., its last digit is 0, 2, 4, 6, or 8.
• A number is divisible by 6 if it meets two conditions: it is divisible by 2 (i.e., it is even) and divisible by 3.
• A number is divisible by 3 if the sum of its digits is divisible by 3.

Now, let's analyze the implication of these rules:

Since a number divisible by 2 is even, it satisfies the first condition for divisibility by 6. However, it still needs to meet the second condition—divisibility by 3—to be divisible by 6. This implies that not all even numbers (divisible by 2) are multiples of 3.

For example, consider the number 4:

• 4 is divisible by 2 because it is even.
• However, 4 is not divisible by 3 because the sum of its digits (4) is not divisible by 3.
• Therefore, 4 is not divisible by 6 because it doesn't meet both required conditions.

Therefore, understanding the definitions, we can see that a number divisible by 2 is not necessarily divisible by 6. These two criteria must both be met for a number to be divisible by 6. Consequently, the correct answer is "No".

In conclusion, a number being divisible by 2 does not guarantee that it is divisible by 6.