다음을 풀어보세요: 70!*70!/80!*60!

$$\frac{ 70 ! \times 70 ! }{ 80 ! \times 60 ! }$$

계산

$$\frac{346769689}{1439241355}\approx 0.24093922$$

해답 단계

70!과(와) 70!을(를) 곱하여 \left(70!\right)^{2}(을)를 구합니다.

$$\frac{\left(70!\right)^{2}}{80!\times 60!}$$

70의 계승은 11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000입니다.

$$\frac{11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000^{2}}{80!\times 60!}$$

11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000의 2제곱을 계산하여 143486179252605282342806635197268128186483973356654097161524529227261957403344906950524588163677475732975695571390639580290806725956789181304836309777641976540401395302400000000000000000000000000000000을(를) 구합니다.

$$\frac{143486179252605282342806635197268128186483973356654097161524529227261957403344906950524588163677475732975695571390639580290806725956789181304836309777641976540401395302400000000000000000000000000000000}{80!\times 60!}$$

80의 계승은 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000입니다.

$$\frac{143486179252605282342806635197268128186483973356654097161524529227261957403344906950524588163677475732975695571390639580290806725956789181304836309777641976540401395302400000000000000000000000000000000}{71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000\times 60!}$$

60의 계승은 8320987112741390144276341183223364380754172606361245952449277696409600000000000000입니다.

$$\frac{143486179252605282342806635197268128186483973356654097161524529227261957403344906950524588163677475732975695571390639580290806725956789181304836309777641976540401395302400000000000000000000000000000000}{71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000\times 8320987112741390144276341183223364380754172606361245952449277696409600000000000000}$$

71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000과(와) 8320987112741390144276341183223364380754172606361245952449277696409600000000000000을(를) 곱하여 595528529747859576732551720067744655471974906375437967027891579389978351058077643608066119727979258178207029727548544024718296431927079222747502820344753912504981127168000000000000000000000000000000000(을)를 구합니다.

$$\frac{143486179252605282342806635197268128186483973356654097161524529227261957403344906950524588163677475732975695571390639580290806725956789181304836309777641976540401395302400000000000000000000000000000000}{595528529747859576732551720067744655471974906375437967027891579389978351058077643608066119727979258178207029727548544024718296431927079222747502820344753912504981127168000000000000000000000000000000000}$$

413779473247459302427112178184835896041894173041906489011283016801569289994503836090831422592063621030544268739101471986759508054802301885459303537275548834201600000000000000000000000000000000을(를) 추출 및 상쇄하여 분수 \frac{143486179252605282342806635197268128186483973356654097161524529227261957403344906950524588163677475732975695571390639580290806725956789181304836309777641976540401395302400000000000000000000000000000000}{595528529747859576732551720067744655471974906375437967027891579389978351058077643608066119727979258178207029727548544024718296431927079222747502820344753912504981127168000000000000000000000000000000000}을(를) 기약 분수로 약분합니다.

$$\frac{346769689}{1439241355}$$

인수 분해

$$\frac{7 \cdot 17 \cdot 23 \cdot 31 \cdot 61 \cdot 67}{5 \cdot 19 \cdot 37 \cdot 71 \cdot 73 \cdot 79} = 0.24093921967660525$$