Finding number of members in set

[juandiaz]

Please suggest me solving this problem.

 

[Dr.Peterson]

Please suggest me solving this problem.

I would start by rephrasing the problem something like this:

Find the number of ordered pairs (a,b) such that a < b, a and b are relatively prime, and their product is 30!.​

I haven't tried solving it yet, but I suspect it will be helpful to find the prime factorization of 30! (or at least to imagine doing so). How might you use that to choose a pair that meets the criteria?

Now it's your turn: Please follow our guidelines and tell us what ideas you already have, so we can help you use what you know.

 

[juandiaz]

View attachment 31035

I would start by rephrasing the problem something like this:

Find the number of ordered pairs (a,b) such that a < b, a and b are relatively prime, and their product is 30!.​

I haven't tried solving it yet, but I suspect it will be helpful to find the prime factorization of 30! (or at least to imagine doing so). How might you use that to choose a pair that meets the criteria?

Now it's your turn: Please follow our guidelines and tell us what ideas you already have, so we can help you use what you know.

Thank youso much.