There are two kinds of half-life questions.....

The first are ridiculously easy, like this one, where you have a small integer number of half-lives, in this case 4.

26 hr / 6.5 hr = number of half-lives

n --> n/2 --> n/4 --> n/8 --> n/16 ... amount of radionuclide left (n is the original amount)

.....1 ........2.........3...........4 ............ number of half-lives

Then, there are the realistic problems where there are more real-world situations. Radioactive decay is a first-order process and is described by this equation.

A = Ao e^(-kt) ...... where A and Ao are amounts, t is the elapsed time and k is the decay constant which is related to the half-life. k = ln2 / t½. (k = ln2 / 6.5hr) = 0.107 hr⁻¹)

A = Ao e^(-0.107 hr⁻¹ x 26 hr)

A = Ao (0.0625)

Since 0.0625 is the equivalent of 1/16, the answers to both methods are the same. Of course, if we knew what the original amount (Ao) of the isotope was we could get a more definitive answer.