Question

La imparitea numerelor 225 267 288 cu acelasi numar natural se obtin resturile 5 7 si respectiv 8.Determinati impartitorul!

Answer 1

225 : i = x rest 5

267 : i = y rest 7

288 : i = z rest 8


=> ix = 225 - 5 = 220

=> iy = 267 - 7 = 260

=> iz = 288 - 8 = 280


220 = 2^2 × 5 × 11

260 = 2^2 × 5 × 13

280 = 2^3 × 5 × 7
________________

cmmdc = 2^2 × 5 = 20

impartitorul = 20
_____________


225 : 20 = 11 rest 5

267 : 20 = 13 rest 7

288 : 20 = 14 rest 8