Question

g.c.d. of 28 and 49 and express it as a linear combination of 28 and 49

Answer 1

Answer:

7=2(28)-1(49)

Step-by-step explanation:

g.c.d. of 28 and 49 and express it as a linear combination of 28 and 49

.......1

.....________

28|..49

....|..28

....|..-------

....|..21

...........1

......________

21|..28

....|..21

....|--------

....|....7

.........3

...--------------

7|..21

..|..21

..|..--------

..|...0

Now, we have

49=1(28)+21........(1)

28=1(21)+7..........(2)

21=3(7)+0...........(3)

(2) can be written as

7=28-1(21)

7=28-1[49-1(28)] (using (1))

7=2(28)-1(49)