Using prime numbers, which number can be added to 12 to obtain a new number with fewer prime factors?

To determine which number can be added to 12 to create a new number with fewer prime factors, we first need to understand the prime factors of the resultant numbers.

Starting with 12, it has the prime factorization of (2^2 \times 3^1). This means it has a total of three prime factors: 2, 2, and 3.

Now, let’s consider each option when added to 12:

1. Adding 6:

• (12 + 6 = 18)

• The prime factorization of 18 is (2^1 \times 3^2), which has a total of three prime factors: 2, 3, and 3.

2. Adding 5:

• (12 + 5 = 17)

• The prime factorization of 17 is simply 17 itself, which is a prime number. Therefore, it has only one prime factor.

3. Adding 8:

• (12 + 8 = 20)

• The prime factorization of 20 is (2^2 \times 5^1), which has three prime factors: 2,