Final answer:
The Greatest Common Factor (GCF) of 24 and 36 is 12. When the sum 24+36 is expressed as a product of the GCF, it becomes 12 x (2 + 3), which simplifies to 60.
Step-by-step explanation:
To find the Greatest Common Factor (GCF) of 24 and 36, we list their factors to identify the largest number that divides both without any remainder.
For 24, the factors are 1, 2, 3, 4, 6, 8, 12, 24. For 36, the factors are 1, 2, 3, 4, 6, 9, 12, 18, 36.
The GCF is therefore 12. Next, to rewrite the sum 24 + 36 as a product of the GCF and a new sum, we express each number as a multiple of the GCF (24 = 2 x 12, 36 = 3 x 12).
Now we have:
(2 x 12) + (3 x 12) = 12 x (2 + 3)
= 12 x 5
= 60.
So, the sum 24+36, when re-written as a product of the GCF 12, becomes 12 x 5, which equals 60.