Question

The total number of ways in which 18900 can be split in 2 factors which are relative ptime are

Answer 1

Answer:

Step-by-step explanation:

For 1, all the factors of each prime have to stay together, otherwise the two factors will not be coprime. You can consider it to be 18900=4×27×25×7 One factor will be the product of some subset of {4,27,25,7} and the other factor will be all the rest. Each factorization gets counted twice, once when each factor is the first one selected.

For 2, we don't have the requirement of coprime. For the factors of 2, you can have any number of 2's from 0 through 4, so there are five choices. This is where the (4+1) comes from. If 94864 were not a square, the product of the number of factors plus one would be even. Again we would divide by 2 because you can choose each factorization in two ways. The +1 comes because it is a square, so you can only choose the factorization of two square roots in one way

Answer 2

Step-by-step explanation:

18900=2²×3³×5²×7.

So no. of Different prime factors in 18900 is 4, i.e 2,3,5,7

So no. of ways in which 18900 can be resolved

18900 into product of 2 relatively prime factors is =2⁴/2=8.