Final answer:
The sum of 36 + 48 can be rewritten as 12(3 + 4), given that 12 is the greatest common factor (GCF) of both numbers, resulting in the product 12 * 7.
Step-by-step explanation:
Factoring Out the Greatest Common Factor (GCF)
To rewrite the sum 36 + 48 as a product of the GCF and another sum, first, find the greatest common factor of the two numbers. The GCF of 36 and 48 can be determined by listing the factors of each number or using the Euclidean algorithm. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The largest common factor is 12.
Next, you divide both numbers by the GCF. This gives us 36 ÷ 12 = 3 and 48 ÷ 12 = 4. The sum of 36 + 48 can be rewritten as 12(3 + 4), which simplifies to 12 × 7.