If an odd number p divides q2 then will it divide q3 also?? Explain.

1.	If an odd number p divides q2 then will it divide q3 also?? Explain.
Answer» Smallest odd prime number = 3Smallest odd composite number = 9H.C.F. of (3, 9) = 3L.C.M. of (3, 9) = 9As odd number p divides q².⇒ p is a factor of q² or q²/p gives 0 as a remainder.Now,\xa0q²\xa0× q = q³, and p is a factor of q², hence it will also be a factor of q²\xa0× q.⇒ p is a factor of q³Therefore, p will divide\xa0q³ also.In general, we can say that if p divides q² then it will also divide qⁿ, where n is a natural number (n ≥ 2).

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