For each positive integer k, let ak = 7k. Which of the following is

This is a confusing new GMAT Focus question, so I am going to try to explain it in words rather than math notation whenever possible.

We can agree that the expression being asked about is equal to 7^28 x 28!

It then asks us for the largest power of 10^n for which "10^n divides" the expression: in other words, the largest power of n for which 10^n is a factor of the expression.

Simply put, this means that (expression) / 10^n = integer — not the other way around, a common misinterpretation.

The 7^28 (clearly not a multiple of 10) is not a problem, because it's in the numerator—only the denominator needs to cancel fully for the answer to remain an integer.

Now we simply need to see how many 10s are in 28 factorial (28!).

Break 10 into its prime factorization of 5 and 2, and—since there are obviously plenty of 2s in the numerator—start counting 5s instead: they should be the limiting factor.

In 28! we find exactly six 5s: two in 25, one in 20, one in 15, one in 10, and one in 5. The correct answer is because there are only six fives in 28 factorial (28!).

We will still have a bunch of numbers left in the numerator, of course—including most of 28 factorial, and a whopping 28 sevens—but that's OK, because the answer is still an integer.