Factors 2

$40! = 2^{38} \times 3^{18} \times 5^{9} \times 7^{5} \times 11^{3} \times 13^{3} \times 17^{2} \times 19^{2} \times 23 \times 29 \times 31 \times 37$

$40! = 2^{36} \times 2^{2} \times 3^{18} \times 5^{9} \times 7^{3} \times 7^{2} \times 11^{3} \times 13^{3} \times 17^{2} \times 19^{2} \times 23 \times 29 \times 31 \times 37$

$40! = (2^{3})^{12} \times (3^{3})^{6} \times (5^{3})^{3} \times (7^{3})^{1} \times (11^{3})^{1} \times (13^{3})^{1} \times 2^{2} \times 7^{2} \times 17^{2} \times 19^{2} \times 23 \times 29 \times 31 \times 37$

$(12+1) \times (6+1) \times (3+1) \times (1+1) \times (1+1) \times (1+1)$

$13 \times 7 \times 4 \times 2 \times 2 \times 2 = \boxed{2912}$