The prime factorization of 44 is \(2 \times 2 \times 11\) and the prime factorization of 60 is \(2 \times 2 \times 3 \times 5\).

Now, let's find the union (\(\cup\)) and intersection (\(\cap\)) of the prime factors:

- \(X \cup Y\) (union): The elements that appear in either set \(X\) or set \(Y\).

- \(X \cap Y\) (intersection): The elements that appear in both set \(X\) and set \(Y\).

**Prime Factors of 44 (X):** \(2, 2, 11\)

**Prime Factors of 60 (Y):** \(2, 2, 3, 5\)

- \(X \cup Y = \{2, 2, 3, 5, 11\}\) (duplicate elements are kept once)

- \(X \cap Y = \{2\}\)

So, the elements of \(X \cup Y\) are \{2, 3, 5, 11\} and the elements of \(X \cap Y\) are \{2\}.