Question

In cate zerourise termina numarul:1×2×3×4.....×74×75?
Am nevoie mare de ajutor!

Answer 1

$75:5=15 \\ 75:25=3 \\ ------ \\ \\ Deci~numarul~se~termina~in~15+3=18~zerouri. \\ \\ Pentru~a~afla~in~cate~cifre~de~zero~se~termina~numarul~ \\ 1 \cdot 2 \cdot 3 \cdot ... \cdot n~trebuie~sa~calculam: \\ \\ \Big [ \frac{n}{5} \Big ] + \Big [ \frac{n}{5^2} \Big ] + \Big [ \frac{n}{5^3} \Big ] +...+ \Big [ \frac{n}{5^a} \Big ],~unde~[x]~este~partea~intreaga~a ~ \\ numarului~real~x.$

Answer 2

1x2x3x...10 = 2 zerouri (de la inmultirea cu 10 si de la 2x5)
11x12x...20 = 2 zerouri (14x15 si inmultirea cu 20)
21x22x...30 = 3 zerouri (24x25 = 600 si inmultirea cu 30)
31x32x...x40 = 2 zerouri
41x42...x50 = 3 zerouri
51x52x...x60 = 2 zerouri
61x62x...x70 = 2 zerouri
71x72x,,,x75 = 2 zerouri
rezulta 18 zerouri