Hi

niks18 VeritasKarishma chetan2u Bunuel PKNIs the question based on prime factorization of positive integers?

If r and s are positive integers, is the greatest prime factor of r larger than the greatest prime factor of s?

**Quote:**

(1) r = 11^s

I initially thought that any prime no raised to any positive exponent will have same no of prime factors

as the no itself.

e.g. 11^s where s is positive integer will have same no of prime factors as 11.

So suff. prime factors of r and s are same: 1 and 11

But statements also opens up the possibility of s being a composite no.

E.g. 11^38; 38 which is 19*2

Now prime factors of s: 19, 2 and r: 11,19,2; r has more prime factors than s

So St 1 is insuff

**Quote:**

(2) r/s>1

r>s

r=4, s =2 , prime factors of r and s are equal

r=6, s =2 , prime factors of r(2,3) are more than s (2)

St Insuff

Combining St 1 and St 2

Now, this got trickier.

A prime no raised to any positive integer does not add any value to fact:

the prime no raised to exponent is greater than the prime no itself.

What is the use of St 2 while combining with St 1?

How do I link this to prime factorization of the number itself?

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