Answer
gcd( 6664, 765) = 17
The linear combination of 6664 and 765 is :
17 = -7(6664) + 61(765)
Work Step by Step
First, caculate the gcd( 6664, 765 )
6664 = 765 * 8 + 544
765 = 544*1 + 221
544 = 221*2 + 102
221 = 102*2 + 17
102 = 17 * 6 + 0
Therefore, the gcd( 6664, 765 ) = 17
Then, express 17 as a linear combination of 6664 and 765 using the extended Euclidean algorithm
17 = 221 – 102*2
= 221 – ( 544 – 221 * 2 ) * 2
= 221 – 544 * 2 + 221*4
= 544 * ( -2 ) + 221*5
= 544 * ( -2 ) + ( 765 - 544*1 ) *5
= 544 * ( -2 ) + 765 *5 - 544 *5
= 765 *5 + 544 * ( -7 )
= 765 *5 + ( 6664 - 765 * 8 ) * ( - 7 )
= 6664 * ( - 7 ) + 765 * 61
Therefore, the linear combination of 6664 and 765 is :
17 = -7(6664) + 61(765)
