Can a number such as 10 have infinite factors if we include multiplying two rational numbers or a rational number and integer or any other combinations? Google says factors of 10 are 1×10, 2×5 and the number of factors is finite but isn't 2.5×4 also a factor of 10 and infinite more?.
2026-04-24 09:47:56.1777024076
Can a number have infinite number of factors if we include rational numbers
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1
It depends more on what you define a factor to be.
In the context of number theory it might suit you better to define a factor as an element in the ring which divides your number or if you work in a UFD a factor is a prime (or combination of such) which appears in the unique factorization. In this case, speaking of the ring $\mathbb(Z)$ you obviously can only have a finite amount of factors for any integer such as $10$.
If you include rational numbers in your definition of factor it obviously looks a bit different. You can find infinite factorizations into two rational numbers for any given rational.
For example with 10 you get $\frac{1}{2}*20, \frac{1}{3}*30, \frac{1}{4}*40$ and so on. And theres even infinite more.
So your question more or less boils down to what you take as a definition for the word "factor". In different fields of maths it can make sense to define this term differently