Question

Using euclids algorithm find the hcf of 1190 and 1445 .and express in the form of 1990m+1445n

Answer 1

Hey

By Euclid's Algorithm, we write :

→ 1445 = 1190 x 1 + 255

→ 1190 = 255 x 4 + 170

→ 255 = 170 x 1 + 85

→ 170 = 85 x 2 


=> Since 85 divides 170 completely, it divides the whole system

=> 85 is the HCF

♦ Tracing the other way :

→ 85 = 255 - 170

= 255 - ( 1190 - 255 x 4 )

= ( 1445 - 1190 ) x 5 - 1190 

= ( 1445 )5 - 1990 x 6

→ Comparing this with : 1190 m + 1445n, 

☻☻ m = -6 , n = 5 is the solution