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1 solution
The prime factorization of 1 0 ! is 2 8 ∗ 3 4 ∗ 5 2 ∗ 7 .
Thus the number of (positive) factors is
( 8 + 1 ) ( 4 + 1 ) ( 2 + 1 ) ( 1 + 1 ) = 2 7 0 .
An explanation of this calculation is given here .