IIT JEE , AIEEE Forum - Mathematics , Algebra

bhuwanaroracorroded

no. of ways in which a composite no. N can be resolved into two factors which are relatively prime to each other is equal to

1 2^n-1

2 2^n-2

3 2ⁿ

4 none of these

nadeemoidu

It is 1) 2^{n-1
where n is the no. of prime factors of N.}Let N= p₁^a1 p₂^a2....p_n ^anEach prime factor can either go to the first factor or the second factor. since the two factors are relatively prime ,we cannot choose the power of p_i in a factor.
If a factor say p₁ is going to the first factor, then p₁should completely go to the first factor and so on. So the no. of ways is 2ⁿ

Finally , each factorization appears 2 times ( ab and ba) so we divide the answer by 2.

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