Answer:
15
Explanation:
We can start by trying to figure out the divisors for each number. A divisor is a whole number that we can multiply by another whole number to equal our target number.
For example, 2's divisors would be 2 and 1, because we can multiply 2 and 1 together to get 2.
30's divisors would be: 1, 30, 2, 15, 3, 10 4, 5, 6
45's divisors would be: 1, 45, 3, 15, 5, 9
75's divisors would be: 1, 75, 3, 25, 5, 15
We should start with 30's divisors because we're searching for a greatest common divisor, so we have to make sure that divisor still fits into the smallest number. Additionally, we should go from biggest to smallest because by eliminating the highest possibilities first, we can ensure that our answer will be the biggest possible one without having to check every single one.
30's biggest divisor is 30, but neither 45 nor 75 have it. 30's next biggest divisor is 15, and that is a common divisor between 45 and 75. Since we worked from the biggest to the smallest, we also know that it is the highest possible common divisor.
That means the G.C.D. of 30, 45, and 75 is 15.