Question

Sa se determine cu cate zerouri se termina scrierea zecimala a numarului 47! .

Answer 1

5=1*5⇒un 5
10=2*5⇒un 5
15=3*5⇒un 5
20=4*5⇒un 5
25=5*5⇒doi de 5
30=6*5⇒un 5
35=7*5⇒un 5
40=8*5⇒un 5
45=9*5⇒un 5
Total: 10 de 5
Produsul se termina in 10 zerouri

Answer 2

$\hbox{Pentru a determina nr. de zerouri ale unui produs de forma:} \\\\ 1*2*3*...*n \\\\ \hbox{se foloseste formula:} \\\\ \ [ \frac{n}{5} ]\ +[ \frac{n}{5^1}]+[\frac{n}{5^2}]+... \\\\ \hbox{ unde [ ] reprezinta partea intreaga a nr.} \\\\\\ 47!=1*2*3*....*47 \\\\ \\ Nr. \ de \ zerouri \ ale \ nr. \ 47! \ este: \\\\\\ \ [\frac{47}{5} ]+ [\frac{47}{25}]+[\frac{47}{125}]+... \\\\ N=9+1+0+... \\\\ \boxed{N=10 \ zerouri}$