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Chapter 7: Problem 1

Even integer n is divisible by 3. What can you say about n?

Short Answer

Expert verified
If an even number \(n\) is divisible by 3, it must be a multiple of 6.

Step by step solution

01

Understanding the properties of even numbers

An even number is any integer that can be expressed in the form \(2k\), where \(k\) is an integer. So \(n=2k\).
02

Establishing relation with divisibility by 3

The problem statement asserts that \(n\) is divisible by 3, this implies \(n=3m\) where \(m\) is another integer.
03

Determining the relation between \(k\) and \(m\)

Since \(n=2k\) and also \(n=3m\), it must be that \(2k=3m\). From this equation, it can be inferred that \(k\) must be a multiple of 3.
04

Conclusion

Considering the information from steps 2 and 3, it can be deduced that if \'n\' is an even number and is divisible by 3, then \'n\' must be a multiple of 6.

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