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Understanding the rule of divisibility by 2 is quite simple. A number is divisible by 2 if it is an even number. This means that the last digit of the number must be 0, 2, 4, 6, or 8. Let's see how this applies:

• 702 ends in 2, making it even and therefore divisible by 2.
• 168 ends in 8, also even, thus divisible by 2.
• 678 ends in 8, again an even number, so it passes this test.
• 658 ends in 8, ensuring it's even and divisible by 2.

This check was important for determining if each number in the exercise was a candidate for being divisible by 6.

Divisibility by 3 relies on a different kind of check. To determine if a number is divisible by 3, sum the digits of the number. If the sum is divisible by 3, then the original number is as well. Let's break this down with the given numbers:

• For 702, add 7 + 0 + 2 = 9. Nine is divisible by 3.
• For 168, calculate 1 + 6 + 8 = 15. Fifteen is divisible by 3.
• For 678, the sum is 6 + 7 + 8 = 21. Twenty-one is divisible by 3.
• For 658, add 6 + 5 + 8 = 19. Nineteen is not divisible by 3.

Only 658 fails this test, identifying it as a number that isn't divisible by 3 and hence, not divisible by 6 either.

Even numbers are key to understanding many divisibility rules because they are always divisible by 2. An even number is simply any integer that ends with a digit of 0, 2, 4, 6, or 8.

These numbers follow the rule of divisibility by 2 as discussed above, and they ensure that we can further test these numbers for divisibility by other factors like 3 or 6. Recognizing even numbers quickly helps in performing quick and accurate calculations, particularly in problems like these where divisibility by multiple numbers is being evaluated.

Remember, while being even means a number is easily divisible by 2, to be divisible by multiple numbers such as 6, it must meet additional criteria, like divisibility by 3 for this specific exercise.