Explanation:
To rewrite (24 + 40) as an integer times the sum of two integers, Gracie first factored out 2, obtaining:
(24 + 40) = 2 × (12 + 20)
We can check that this is true by distributing the 2:
2 × (12 + 20) = 2 × 12 + 2 × 20 = 24 + 40
Now, Gracie is looking for other numbers greater than 2 that she can factor out of (24 + 40) to rewrite the expression as an integer times the sum of two integers.
One way to approach this is to look for other common factors between 24 and 40. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. The common factors of 24 and 40 are 1, 2, 4, 8, and the largest factor is 8.
Therefore, Gracie can factor out 4 or 8 to rewrite the expression as an integer times the sum of two integers. For example:
(24 + 40) = 4 × (6 + 10)
(24 + 40) = 8 × (3 + 5)
Note that we can also factor out 1 or 2, but that would not change the expression in any meaningful way.