Solve 69!/12^40

$$\frac { 69 ! } { 12 ^ { 40 } }$$

Evaluate

$$\frac{1251546905693700108986672256005352587905812203977624298095703125}{107495424}\approx 1.16427924 \cdot 10^{55}$$

Solution Steps

The factorial of 69 is 171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000.

$$\frac{171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000}{12^{40}}$$

Calculate 12 to the power of 40 and get 14697715679690864505827555550150426126974976.

$$\frac{171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000}{14697715679690864505827555550150426126974976}$$

Reduce the fraction \frac{171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000}{14697715679690864505827555550150426126974976} to lowest terms by extracting and canceling out 136728756748667408445475367864500224.

$$\frac{1251546905693700108986672256005352587905812203977624298095703125}{107495424}$$

Factor

$$\frac{5 ^ {15} \cdot 7 ^ {10} \cdot 11 ^ {6} \cdot 13 ^ {5} \cdot 17 ^ {4} \cdot 19 ^ {3} \cdot 23 ^ {3} \cdot 29 ^ {2} \cdot 31 ^ {2} \cdot 37 \cdot 41 \cdot 43 \cdot 47 \cdot 53 \cdot 59 \cdot 61 \cdot 67}{2 ^ {14} \cdot 3 ^ {8}} = 1.1642792401039324 \times 10^{55}\frac{106135552}{107495424} = 1.1642792401039324 \times 10^{55}$$