Proof of Divisibility By 6

After discussing divisibility by 5, we proceed to divisibility by 6. A number is divisible by 6 if

(1) it is even
(2) it is divisible by 3

The explanation to this is quite simple. First, if a number is even, then it is divisible by 2.

Let n be that number. Since n is even, then we can write it in a form two times another integer, say k. That is,

n = 2k.


Now, looking at condition 2, a number is divisible by 6 if it is also divisible by 3. This means that k must be divisible by 3 since 2k is divisible by 3. Now, if k is divisible by 3, then we can write it as 3 multiplied by another integers, say, h. That is,

k = 3h.

Combining the first and second equations, we have

n = 2k = 3(2h)

This means that n = 6h which is clearly divisible by 6.

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