Final answer:
To find the sum of 24 and 36 using the GCF and Distributive Property, identify the GCF as 12, then express the sum as 12 multiplied by the sum of 2 and 3, resulting in a final sum of 60.
Step-by-step explanation:
To find the sum of 24 and 36 using the Greatest Common Factor (GCF) and the Distributive Property, we first need to determine the GCF of these two numbers. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24; the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The GCF for 24 and 36 is 12 since it is the largest number that appears in both lists of factors.
Next, using the Distributive Property, we write the sum as a product of the GCF and the sum of the remaining factors after dividing each number by the GCF:
24 + 36 = (12 × 2) + (12 × 3) = 12 × (2 + 3) = 12 × 5
Now, just multiply the GCF, which is 12, by 5, to get:
12 × 5 = 60
Therefore, the sum of 24 and 36, using the GCF and the Distributive Property, is 60.