Find the greatest common factor of 42, 126 and 210.

• A. 2
• B. 6
• C. 14
• D. 21
• E. 42

To find the greatest common factor (GCF) of the numbers 42, 126, and 210, we can start by determining the prime factorization of each number.

Prime Factorization

• 42: 2 × 3 × 7
• 126: 2 × 3 × 3 × 7 (or 2 × 3² × 7)
• 210: 2 × 3 × 5 × 7

Identifying Common Factors

Next, we look for the factors that are common to all three numbers. The prime factors they share are:

• 2
• 3
• 7

Calculating the GCF

Now, we multiply the lowest powers of these common prime factors:

• 2¹ (from all three numbers)
• 3¹ (from all three numbers)
• 7¹ (from all three numbers)

So, the GCF is:

GCF = 2 × 3 × 7 = 42

Final Answer

The greatest common factor of 42, 126, and 210 is 42. Therefore, the correct choice is E. 42.