Question

Find the HCF of 456 and 256 by Euclid's division lemma

Answer 1

according to Euclid division lemma ,
a = bq + r

now,

step for finding HCF of 456 and 256
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use a = bq + r for 456 and 256

456 = 256 ×1 + 200
remainder 200 so,

again use Euclid lemma for 256 and 200

256 = 200× 1 + 56
remainder 56 so,

agian use Euclid lemma for 200 and 56

200 = 3 × 56 + 32

remainder 32 so,

again E. D lemma , for 56 and 32

56 = 1 × 32 + 24

again E.D lemma for 32 and 24

32 = 1× 24 + 8

again E.D lemma for 24 and 8

24 = 8 ×3 + 0

here remainder zero so,
HCF of 456 and 256 = 8

Answer 2

456=256(1)+200
256=200(1)+56
200=56(3)+32
56=32(1)+24
32=24(1)+8
24=8(3)+0
hcf=8