Question

The product of the first 101 positive integers is divided by the product of the first 100 positive integers. How many positive integer factors does the quotient have?

Answer 1

$(1\cdot2\cdot3\cdot4\cdot...\cdot101):(1\cdot2\cdot3\cdot4\cdot...\cdot100)\\\\=\dfrac{1\cdot2\cdot3\cdot4\cdot...\cdot100\cdot101}{1\cdot2\cdot3\cdot4\cdot...\cdot100}=101\\\\101-is\ the\ prime\ number\\\\Answer:\ Two\ positive\ integer\ factors:\ 1\ and\ 101.$