To solve this problem by finding the GCF of 75 and 90, it is easiest to begin by listing out the factors of both of these numbers. To find the factors, begin with 1 and work towards your number, testing if your number is evenly divisible. If it is, make sure you record both numbers that multiplied to give you your product.
The factors of 75 are: 1, 3, 5, 15, 25, and 75
The factors of 90 are: 1, 2, 3, 5, 6, 15, 18, 30, 45, 90
Now, we must find the greatest shared number between these two lists. In this case, that number is 15.
The next part of the question asks us to write each number as a product of the GCF. To do this, we must simply go back to our list of factors and see which other factor pairs with 15 to give you a total of 90.
75/15 = 5
90/15 = 6
Therefore, because our original problem was 75 + 90, we can rewrite this as:
(5 * 15) + (6 * 15)
If we use the distributive property to rewrite this, we must pull out the shared factor from both parentheses, which leaves the addition problem. This is modeled below:
15 (5 + 6)
Therefore, your final answer is that the GCF is 15, and the second part should appear as follows:
(5 * 15) + (6 * 15) = 15(5 +6)
Hope this helps!