Proof of Divisibility of 8 rule

In summary, the conversation discusses using a direct proof to prove a conditional statement about natural numbers and divisibility by 8. The conversation also mentions using the lowest power of 10 that is divisible by 8 in the proof.
  • #1
smiles988
6
0

Homework Statement


Let n be a natural number. If the number formed by the last three digits of n is divisible by 8, then n is divisible by 8.


Homework Equations


Natural numbers are the set of {1,2,3,4,5,6,...}


The Attempt at a Solution


I believe we should use a direct proof to prove this conditional statement. Thus we will assume that n is a natural number and the number formed by the last three digits of n is divisible by 8. We will prove that n is divisible by 8.
I don't know where to go from here. Please help!
 
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  • #2
Hint: What is the lowest power of 10 that is divisible by 8?
 
  • #3
Reply to Hint

Okay so 1000 is the lowest power of 10 that is divisible by 8. How do I use that?
 

FAQ: Proof of Divisibility of 8 rule

What is the "Proof of Divisibility of 8 rule"?

The "Proof of Divisibility of 8 rule" states that a number is divisible by 8 if the last three digits of the number are also divisible by 8. This is a rule commonly used in mathematics to determine divisibility.

How do you use the "Proof of Divisibility of 8 rule"?

To use the "Proof of Divisibility of 8 rule", you simply need to check if the last three digits of a number are divisible by 8. If they are, then the entire number is divisible by 8. If they are not, then the number is not divisible by 8.

Can the "Proof of Divisibility of 8 rule" be applied to any number?

Yes, the "Proof of Divisibility of 8 rule" can be applied to any number. It is a universal rule for determining divisibility by 8.

Why is the "Proof of Divisibility of 8 rule" useful?

The "Proof of Divisibility of 8 rule" is useful because it provides a quick and easy way to determine if a number is divisible by 8. This can be helpful in simplifying mathematical calculations and identifying patterns in numbers.

Are there other rules for determining divisibility besides the "Proof of Divisibility of 8 rule"?

Yes, there are other rules for determining divisibility by different numbers, such as the "Proof of Divisibility of 2 rule" and the "Proof of Divisibility of 3 rule". These rules are based on different factors and are used for different purposes.

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