# A question regarding multiples of 3

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• guifb99
In summary, the conversation discusses why odd multiples of 3 cannot result in a natural number when plugged into the expression "24-1(x2-1)=y". The individual asking the question clarifies that it is not "1/2" but "1/24" in the expression. The conversation also includes a request for a better explanation using an example and a question about whether this is a homework assignment. Finally, the conversation ends with the individual providing a clearer explanation and asking a follow-up question.
guifb99
Why doesn't any odd multiple of 3 can give "24-1(x2-1)=y" as a result (y) a natural number? Obviously no even number will make "y" a natural number, but all of the odd numbers do, but odd multiples of 3 (3, 9, 15, 21, 27...).

x=1⇒y=0
x=3⇒y=1/3
x=5⇒y=1
x=7⇒y=2
x=9⇒y=10/3
x=11⇒y=5
x=13⇒y=7
x=15⇒y=28/3
x=17⇒y=12
x=19⇒y=15
x=21⇒y=55/3
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Last edited:
Can you explain this better perhaps by using an example?

jedishrfu said:
Can you explain this better perhaps by using an example?
I'm sorry, I typed it wrongly, it's not "1/2", it's "1/24".

Okay, but can you explain this better perhaps by using an example?

Is this a homework assignment?

jedishrfu said:
Okay, but can you explain this better perhaps by using an example?

Is this a homework assignment?
There, now I think it's WAY better understandable. I'm sorry. Lol

guifb99 said:
Why doesn't any odd multiple of 3 can give "24-1(x2-1)=y" as a result (y) a natural number? Obviously no even number will make "y" a natural number, but all of the odd numbers do, but odd multiples of 3 (3, 9, 15, 21, 27...).
You mean, why does the expression:
$$\frac{1}{24}(x^2-1)$$
not return an integer when ##x## is an odd multiple of 3? Think about what "odd multiple of 3" means mathematically and substitute that for ##x## in the expression above to see what you get.

Can x2-1 be divisible by 3 if x is divisible by 3?

## 1. What is the definition of a multiple of 3?

A multiple of 3 is a number that can be evenly divided by 3 without any remainder.

## 2. How do I determine if a number is a multiple of 3?

To determine if a number is a multiple of 3, you can use the divisibility rule for 3, which states that if the sum of the digits of a number is a multiple of 3, then the number itself is also a multiple of 3.

## 3. Can a negative number be a multiple of 3?

Yes, negative numbers can also be multiples of 3. As long as the number can be divided evenly by 3, it is considered a multiple of 3.

## 4. What are the first 10 multiples of 3?

The first 10 multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.

## 5. How are multiples of 3 used in mathematics?

Multiples of 3 are commonly used in mathematics to solve problems involving division, fractions, and finding common factors between numbers. They are also used in various mathematical patterns and sequences.

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