[tex]2^{44}\times25^2\times7^4=\\
=2^{44}\times(5^2)^2\times7^4=\\
=2^{44}\times5^4\times7^4=\\
=2^{40+4}\times5^4\times7^4=\\
=2^{40}\times 2^4\times5^4\times7^4 =\\
=2^{40}\times(2^4\times5^4)\times7^4=\\
=2^{40}\times(2\times5)^4\times7^4=\\
=2^{40}\times10^4\times7^4=\\
=2^{40}\times7^4\times10^4=\\
=2^{4\times10}\times7^4\times10^4=\\
=(2^4)^{10}\times7^4\times10^4=\\
=16^{10}\times7^4\times10^4=\\
=16^{10}\times7^4\times10000\\\\
U(16^{10})=6 \\
U(7^4)=1
[/tex]
Unde U() inseamna ultima cifra.
⇒ Ultimele 5 cifre ale numarului sunt:
6 × 1 × 10000 = 60000
Rezulta ca numarul se termina in 4 zerouri
