Question

determinați in cate zerouri se termina produsul primelor 57 de numere naturale nenule .
va rog este urgentttt va dau coroană ​

Answer 1

Hai sa grupam cele 57 de numere astfel:

5*10*15*20*25*30*35*40*45*50*55*1*2*3*4*6*7*8*9*11*12*13*14*16*17*18*19*21*22*23*24*26*27*28*29*31*32*33*34*36*37*38*39*41*42*43*44*46*47*48*49*51*52*53*54*56*57

Hai sa le impartim acum in grupe:

A = 5*10*15*20*25*30*35*40*45*50*55*4*8

B = 1*2*3*6*7*9*11*12*13*14*16*17*18*19*21*22*23*24*26*27*28*29*31*32*33*34*36*37*38*39*41*42*43*44*46*47*48*49*51*52*53*54*56*57

A = 5*(2*5)*(3*5)*(2*2*5)*(5*5)*(2*3*5)*(7*5)*(2*2*2*5)*(9*5)*(2*5*5)*(11*5)*(2*2)*(2*2*2) =

=(5¹³)*( 2¹³)*(3*3*7*9*11) = [(2*5)¹³]*(3*3*7*9*11) = (10¹³)*(3*3*7*9*11)

Notam C = (3*3*7*9*11)

Asadar daca inmultim pe A si B, obtinem:

(10¹³)*B*C, care are 13 zerouri la urma.