Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 345

Can sqrt x be a factor?

Example;

Is sqrt of 9 a factor of 9?

sqrt 9 times sqrt 9 = 9

If so, should we list sqrt when listing the factors of 9?

Should the list be 1,3,9,sqrt 9 (and their negative counterparts, if those count as factors)?

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Can sqrt x be a factor?

hi paulb203

In all the books, lessons and exam papers I have encountered, where 'factor' of an integer has arisen, it has always meant positive whole number(s) that divide exactly. Not to be confused with factorising an expression where different rules apply. **

So, in this context, and as √ 9 = 3, you have already listed it.  If the answer to a question was 1/2 then 0.5, sin(30), and 16/32 would all be equivalent ways of saying the same thing.

** It is always possible, in maths, to make up a new set of axioms and develop a whole new area of maths. The axioms have to be well defined and not contradictory. So I suppose you could introduce negative factors as a concept, but I've never come across it so far.

Bob

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paulb203

Member

Registered: 2023-02-24

Posts: 345

Re: Can sqrt x be a factor?

Hi, Bob.

“...as root 9 = 3, you have already listed it.  If the answer to a question was 1/2 then 0.5, sin(30), and 16/32 would all be equivalent ways of saying the same thing.”

Makes sense. Thanks.

“In all the books, lessons and exam papers I have encountered, where 'factor' of an integer has arisen, it has always meant positive whole number(s) that divide exactly.”
Interesting. I’m discussing this in another thread with Jai Ganesh (“Factors. Can factors be negative numbers?”)

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