If x represents the total number of positive integers that are factors of 240, and y represents the total number of positive integers that are factors of 120, what is the value of x2 y2?
0
2
12
144
256
Solution:
Begin by reducing 240 to its prime factors.
Next, add 1 to each of the exponents and multiply the results: (4 + 1)(1 + 1)(1 + 1) = (5)(2)(2) = 20. Thus, 240 has a total of 20 factors, which means x = 20.
Next, let’s find the prime factorization of 120.
After adding 1 to each exponent and multiplying the results, we get (3 + 1)(1 + 1)(1 + 1) = (4)(2)(2) = 16. Thus, 120 has 16 different factors, which means y = 16.
Finally, we need to determine x2 y2: