Can someone explain this in detail to me please gcd6599d 65x

Can someone explain this in detail to me please?

gcd(65,99)=d. 65x+99y=d. Then d= ,x = , y=

d = gcd (65,99)

65 = 13x5 and 99 = 11x3x3

Hence d = gcd (65,99) = 1 since 1 is the only common factor.

99 = 65x1+34

65 = 34x1+31

34 = 31x1+3

31=3x10+1

Hence (66,95) = 1

we can express gcd of 66, 95, i.e. 1 as

1 =31-3x10

= 65-34-10x3

= 65-34-10(34-65+34)

= 65-34(11)+65(10)-10(34)

= 65(11)-34(21)

= 65(11)-21(99-65)

= -21(99)+32(65)

d = 1, x = 32 and y = -21