Which is the common factor of 32 54 and 66

The Correct Answer and Explanation is:

To find the common factor of 32, 54, and 66, we begin by finding the factors of each number and then identifying the greatest common factor (GCF), which is the largest factor that all three numbers share.

Step 1: Find the factors of 32

The prime factorization of 32 is:
32=2532 = 2^532=25
So, the factors of 32 are: 1, 2, 4, 8, 16, and 32.

Step 2: Find the factors of 54

To find the prime factorization of 54, we divide by 2 and 3:
54=2×3354 = 2 \times 3^354=2×33
So, the factors of 54 are: 1, 2, 3, 6, 9, 18, 27, and 54.

Step 3: Find the factors of 66

To find the prime factorization of 66, we divide by 2 and 3:
66=2×3×1166 = 2 \times 3 \times 1166=2×3×11
So, the factors of 66 are: 1, 2, 3, 6, 11, 22, 33, and 66.

Step 4: Identify the common factors

Now, let’s compare the factors of 32, 54, and 66:

32 has the factors: 1, 2, 4, 8, 16, 32.
54 has the factors: 1, 2, 3, 6, 9, 18, 27, 54.
66 has the factors: 1, 2, 3, 6, 11, 22, 33, 66.

The common factors are: 1, 2.

Step 5: Determine the greatest common factor (GCF)

The greatest common factor is the largest number in the list of common factors. In this case, the greatest common factor is 2.

Conclusion:

The greatest common factor (GCF) of 32, 54, and 66 is 2.