What are factors and multiples?

[Edin_Dzeko]

I'm learning Algebra (the basic and foundation of Math) 'cause I stink. Now I'm just doing some review from the beginning before I get into the tough stuff.

I'm a bit stumped on factors and multiples. I understand it but not clear enough. I couldn't give you a definition and if you asked a tricky enough question, I might get it wrong.

Can someone explain it?

What I understand:

If a question ask what are factors of 20, I'd give numbers that can be divided to 20 and get an even answer. So when I type in 20 in my calculator, and then the "/" the number that I put in after the "/" should give me an even number, if it does, then it's a factor. So ex, I'd go

Factors of 20: {1,2,4,5,10,20}

1x20 = 20
2x10 = 20
5x4 = 20

that's the reason why I wrote 1,2,4,5,10,20 up until I started studying this like today I always that when someone asked that question you'd just say 1,2,5,10,20 I would never have included the 4.

Multiples, based on the example the book I"m using gave, you simple just list the times tables for that specific number ex:

Multiples of 2 = {2,4,6,8,10,12,...}
the book didn't include 1 for the multiples but it did for the factors. So why is that we put 1 for factors and not multiples??

Lastly there was a question:
{y| y is a natural number multiple of 7}

the answer was {7,14,21...}

if it was "y is a WHOLE number multiple of 7" would the zero have been included??

 

[slider142]

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If a question ask what are factors of 20, I'd give numbers that can be divided to 20 and get an even answer.
...

Factors of 20: {1,2,4,5,10,20}

This is the correct definition, assuming you mean "an answer that has no remainder" by "an even answer", and those are all the factors of 20.

up until I started studying this like today I always that when someone asked that question you'd just say 1,2,5,10,20 I would never have included the 4.

Why would you have not included the 4? It fits the exact definition you gave. Mathematics is very precise in this way; there is no leeway given over a definition that is not vague.

Multiples, based on the example the book I"m using gave, you simple just list the times tables for that specific number

That is also a good definition.

the book didn't include 1 for the multiples but it did for the factors. So why is that we put 1 for factors and not multiples??

It does not fit your definition. What position on the 2 times table does 1 occupy? In other words, which multiple of 2 is 1? The first multiple of 2 is 2 (1x2 = 2), the second multiple is 4 (2x2 = 4), and so on.

Lastly there was a question:
{y| y is a natural number multiple of 7}

the answer was {7,14,21...}

if it was "y is a WHOLE number multiple of 7" would the zero have been included??

Yes, 0 is a whole number, and 0*7 = 0. Turn to the definitions for justification.

It is impossible to determine the truth of any mathematical statement if it is not a definition, and thus defined to be true, or follows logically from a collection of definitions. If you find yourself doubting a result, you can only verify whether it is true or false by looking at the definitions or theorems that preceded it.

 

[Edin_Dzeko]

Thank you soooooooooooo much. I really appreciate this. big props