Question

If the HCF of the numbers 30375 and 141750 is of the form a^4 and b^a, then find the values of a and b.

Answer 1

Dear friend

We write given number in prime factors , As :

30375 = 3 × 3 × 3 × 3 × 3 × 5 × 5 × 5

And

141750 = 2 × 3 × 3 × 3 × 3 × 5 × 5 × 5 × 7

Then,

H.C.F. ( 30375 and 141750 ) =  3 × 3 × 3 × 3 × 5 × 5 × 5 =  34 × 5 3  , Compare that with given H.C.F. = a4 × ba and get 

a = 3 and  b  =  5                                                               ( Ans )

Hope this information will clear your doubts about topic.