Question

If d is the HCF of 21658 and 8624, find x, y satisfying d = 8624 x + 21658 y.​

Answer 1

Answer:

x=108

y=-43

Explanation:

First take the HCF of 21648 and 8624 by euclids division lemma

21658=8624×2+4410

8624=4410×1+4214

4410=4214×1+196

4214=196×21+98

196=98×2+0

now,98=4214-(196×21)

=(8624-4410)'(4410-4214)21

=8624-22(4410)+4241(21)

=8264-22(21658-8624×2)+21(8624-4410) =8624-22(21658)+22(8624×2)+21(8624)-21(4410)

=8624-22(21658)+22(8624×2)+21(8624)-21(21658-8624×2

=8624(1+44+21+42)+21658(-22-21)

=8624(108)+21658(-43)