Solve 13!/52*50*51*49*48*47*46*45*44*43*42*41*40

$$\frac{ 13 ! }{ 52 \times 50 \times 51 \times 49 \times 48 \times 47 \times 46 \times 45 \times 44 \times 43 \times 42 \times 41 \times 40 }$$

Evaluate

$$\frac{1}{635013559600}\approx 1.574769522 \cdot 10^{-12}$$

Solution Steps

The factorial of 13 is 6227020800.

$$\frac{6227020800}{52\times 50\times 51\times 49\times 48\times 47\times 46\times 45\times 44\times 43\times 42\times 41\times 40}$$

Multiply 52 and 50 to get 2600.

$$\frac{6227020800}{2600\times 51\times 49\times 48\times 47\times 46\times 45\times 44\times 43\times 42\times 41\times 40}$$

Multiply 2600 and 51 to get 132600.

$$\frac{6227020800}{132600\times 49\times 48\times 47\times 46\times 45\times 44\times 43\times 42\times 41\times 40}$$

Multiply 132600 and 49 to get 6497400.

$$\frac{6227020800}{6497400\times 48\times 47\times 46\times 45\times 44\times 43\times 42\times 41\times 40}$$

Multiply 6497400 and 48 to get 311875200.

$$\frac{6227020800}{311875200\times 47\times 46\times 45\times 44\times 43\times 42\times 41\times 40}$$

Multiply 311875200 and 47 to get 14658134400.

$$\frac{6227020800}{14658134400\times 46\times 45\times 44\times 43\times 42\times 41\times 40}$$

Multiply 14658134400 and 46 to get 674274182400.

$$\frac{6227020800}{674274182400\times 45\times 44\times 43\times 42\times 41\times 40}$$

Multiply 674274182400 and 45 to get 30342338208000.

$$\frac{6227020800}{30342338208000\times 44\times 43\times 42\times 41\times 40}$$

Multiply 30342338208000 and 44 to get 1335062881152000.

$$\frac{6227020800}{1335062881152000\times 43\times 42\times 41\times 40}$$

Multiply 1335062881152000 and 43 to get 57407703889536000.

$$\frac{6227020800}{57407703889536000\times 42\times 41\times 40}$$

Multiply 57407703889536000 and 42 to get 2411123563360512000.

$$\frac{6227020800}{2411123563360512000\times 41\times 40}$$

Multiply 2411123563360512000 and 41 to get 98856066097780992000.

$$\frac{6227020800}{98856066097780992000\times 40}$$

Multiply 98856066097780992000 and 40 to get 3954242643911239680000.

$$\frac{6227020800}{3954242643911239680000}$$

Reduce the fraction \frac{6227020800}{3954242643911239680000} to lowest terms by extracting and canceling out 6227020800.

$$\frac{1}{635013559600}$$

Factor

$$\frac{1}{2 ^ {4} \cdot 5 ^ {2} \cdot 7 ^ {2} \cdot 17 \cdot 23 \cdot 41 \cdot 43 \cdot 47} = 1.5747695224491078 \times 10^{-12}$$