Question

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Write the H.C.F and L.C.M of the smallest odd composite number and the smallest odd prime
number if an odd number P divides q, then will it divide qalso?​

Answer 1

Answer:

Smallest odd prime number = 3

Smallest odd composite number = 9

H.C.F. of (3, 9) = 3

L.C.M. of (3, 9) = 9

As odd number p divides q².

⇒ p is a factor of q² or q²/p gives 0 as a remainder.

Now, 

q² × q = q³, and p is a factor of q², hence it will also be a factor of q² × q.

⇒ p is a factor of q³

Therefore, p will divide q³ 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).