What is the Largest whole number with seven factors?

Answer 1

There is no such largest number.

Take a prime p and raise it to the sixth power.

For example 2^6 = 64 (2 to the 6th power).

Its factors are 1, 2, 4, 8, 16, 32, 64 (seven factors).

Now take any prime p and raise it to the sixth power. Its factors are

1, p, p^2, p^3, p^4, p^5, p^6.

There are infinitely many prime numbers, so p can be as large as you like, and p^6 will be even bigger.