Find the sum of all the common factors of 14 and 28.Multiply the result by the first common multiple of 4 and 8.What is the answer?

1. Break Down the Problem

1. Find all the common factors of 14 and 28.
2. Calculate the sum of these common factors.
3. Determine the first common multiple of 4 and 8.
4. Multiply the sum of the common factors by the first common multiple.

2. Relevant Concepts

• Common Factors: Factors that are common to two or more numbers.
• Least Common Multiple (LCM): The smallest multiple that is exactly divisible by two or more numbers.

3. Analysis and Detail

1. Finding Common Factors of 14 and 28:

   • Factors of 14: $1, 2, 7, 14$
   • Factors of 28: $1, 2, 4, 7, 14, 28$

   Common Factors: $1, 2, 7, 14$

2. Calculating the Sum of Common Factors: $1 + 2 + 7 + 14 = 24$

3. Finding the First Common Multiple of 4 and 8:

   • Multiples of 4: $4, 8, 12, 16, 20, ...$
   • Multiples of 8: $8, 16, 24, ...$

   First Common Multiple: $8$

4. Multiplying the Sum of Common Factors by the First Common Multiple: $24 \times 8 = 192$

4. Verify and Summarize

• The common factors of 14 and 28 are summed to $24$.
• The first common multiple of 4 and 8 was identified as $8$.
• The multiplication of these two results in $192$.

Final Answer

The final result is $192$.