Question

find the greatest common factor of 42 and 28.

Explanation:

Step1: Find factors of 42

The factors of 42 are all the numbers that divide 42 without leaving a remainder. We start from 1:
$1 \times 42 = 42$, $2 \times 21 = 42$, $3 \times 14 = 42$, $6 \times 7 = 42$.
So the factors of 42 are $1, 2, 3, 6, 7, 14, 21, 42$.

Step2: Find factors of 28

Similarly, the factors of 28 are:
$1 \times 28 = 28$, $2 \times 14 = 28$, $4 \times 7 = 28$.
So the factors of 28 are $1, 2, 4, 7, 14, 28$.

Step3: Identify common factors

Now, we find the numbers that are factors of both 42 and 28. From the lists above, the common factors are $1, 2, 7, 14$.

Step4: Determine the greatest common factor

Among the common factors ($1, 2, 7, 14$), the greatest one is 14.

Answer:

14