WolframAlpha lists the factors as 2^38 * 5^38, which is just a compact notation for 38 2s and 38 5s, totalling 76 factors. If you count the 2s and 5s in the output of factor, you get the same result of 38 each for a total of 76 factors.

100000000000000000000000000000000000000

== 10 ^ 38

== (2 * 5) ^ 38

== 2 ^ 38 * 5 ^ 38

== 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5

Are 2 and 5 not prime?