Write the set of even factors of 124.

To find the set of even factors of 124, we first need to determine the prime factorization of 124.

Prime Factorization of 124:

124 is an even number, so it is divisible by 2.
124 ÷ 2 = 62
62 is also divisible by 2.
62 ÷ 2 = 31
31 is a prime number, so the prime factorization of 124 is: 124 = 2² × 31.
Even Factors:

An even factor must include at least one factor of 2. Therefore, the even factors of 124 must have the form 2^k × 31^m, where:
k can be 1 or 2 (because we need at least one 2, but we cannot have more than 2 factors of 2 in the prime factorization of 124).
m can be 0 or 1 (because 31 is a prime factor and can either be included or excluded).
List of Even Factors:

For k = 1 and m = 0: 2¹ × 31⁰ = 2
For k = 1 and m = 1: 2¹ × 31¹ = 62
For k = 2 and m = 0: 2² × 31⁰ = 4
For k = 2 and m = 1: 2² × 31¹ = 124
Thus, the set of even factors of 124 is:

{2, 4, 62, 124}