Question: 1. Consider the number 2020. (a) Find the prime factorization of 2020. (b) Determine the number of positive (integer) divisors of 2020. Hint: You do

1. Consider the number 2020. (a) Find the prime factorization of 2020. (b) Determine the number of positive (integer) divisors of 2020. Hint: You do not need to list the divisors; you only need to count how many there are. 2. What is wrong with the expression 6|12 = 2? Hint: Think about the divides relation (i.e. "|") versus divides operation (i.e. "/" or ). 3. Determine all integers that 0 divides. Hint: It is true that division by zero (the operation) is undefined. This problem asks about the divides relation (so not the divides operation). Think carefully about the definition of the divides relation. A correct response will identify at least one integer. 4. Use the Euclidean algorithm to compute the following gcd's. (a) gcd(2020, 707) (b) gcd(2020, 1776) 5. Let n be any integer. If p is a prime, what are the possible values for gcd(p, n)? Give a brief explanation why your list contains the only possibilities

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