Mr. casey writes the equation 40 = 16 + 24 = a(b + c). what whole
numbers can he choose for a, b, and cif he wants b and c to have no
common factors greater than 1?

Step-by-step explanation:

Given:

Now, in order to write 16 + 24 into a product of two numbers, we need to find the factors of 16 and 24.

Factors of 16 = 1, 2, 4, 8, 16.

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.

Now, common factors for 16 and 24 are 1, 2, 4 and 8.

Now, the values of should be such that there should be no common factors between them except 1. In other words, are prime numbers.

So, in order to get prime numbers for , we should take the greatest common factor for 16 and 24 which is 8.

Therefore 40 = 16 + 24 can rewritten as:

So,

step-by-step explanation: