The selection of how many distinct positive factors of 50 wi

The selection of how many distinct (positive) factors of 50 will guarantee that at least two of them have a product of 50? Explain.

Solution

factors of 50 are 1,2,5,10,25,50.

if we select 2 distinct factors then it will not gaurantee that product will be 50. because product of 2 and 1 is not 50.

now if we select 3 distinct factors then also it won\'t work.

if we select 4 distinct factors then it will gaurantee as we will have two elements whose product will be 50.

suppose if we take 1,2,5,10 then 10 and 5 have product equal to 50.

if we take 5,10,25,50 then 10 and 5 have product equal to 50.

same can be done for other combinations.