If I multiply all whole numbers from 1 through 10 what is the largest power of 4 that is a factor of the product?

If we multiply 1 through 10, the mathematical representation of the product would be,

P = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10

Getting the factors of each number,

P = 1 x 2 x 3 x (2 x 2) x 5 x (3 x 2) x 7 x (2 x 2 x 2) x 9 x (5 x 2)

Then, we take out all the 2's.

2 x (2 x 2) x (3 x 2) x (2 x 2 x 2) x (5 x 2)

Combining all the 2's.

2^8 x 3 x 5

2^8 can also be written as (2 x 2) ^4. Thus, the answer is 4.