Let n be a positive integer. Recall an integer k ≥ 1 is a factor of n if k | n. The integer n is called squarefree if there’s no integer m ≥ 2 such that m2| n. 1 How many positive integer factors does...

Let n be a positive integer. Recall an integer k ≥ 1 is a factor of n if k | n. The integer n is called squarefree if there’s no integer m ≥ 2 such that m2| n.

1 How many positive integer factors does 100 have? How many are squarefree?

2 How many positive integer factors does 12! have? (Hint: calculate the prime factorization of 12!.)

3 How many squarefree factors does 12! have? Explain your answer.