Final answer:
The sum of 42 and 70 can be expressed as the product of their greatest common factor, which is 14, and the sum of their respective factors after division by the GCF, which are 3 and 5. Therefore, 42 + 70 equals 14 × (3 + 5), or 14 × 8, which is 112.
Step-by-step explanation:
To express the sum of the numbers 42 and 70 as a product of their greatest common factor (GCF) and the sum of their respective factors, we first need to find the GCF of 42 and 70. We can list the factors of each number:
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
The common factors are 1, 2, 7, and 14. The greatest of these is 14, which is the GCF. Now we can divide each of the two numbers by the GCF to find their respective factors.
42 divided by 14 is 3
70 divided by 14 is 5
So, we can now express the sum as a product:
42 + 70 = 14× (3 + 5) = 14 × 8
Thus, the sum of 42 and 70 can be written as 14 times 8, which is 112.