Question

find g.c.d of (896,35) by Euclid's method​

Answer 1

Answer:

Set up a division problem where a is larger than b.

a ÷ b = c with remainder R. Do the division. Then replace a with b, replace b with R and repeat the division. Continue the process until R = 0.

2260 ÷ 816 = 2 R 628 (2260 = 2 × 816 + 628)

816 ÷ 628 = 1 R 188 (816 = 1 × 628 + 188)

628 ÷ 188 = 3 R 64 (628 = 3 × 188 + 64)

188 ÷ 64 = 2 R 60 (188 = 2 × 64 + 60)

64 ÷ 60 = 1 R 4 (64 = 1 × 60 + 4)

60 ÷ 4 = 15 R 0 (60 = 15 × 4 + 0)

When remainder R = 0, the GCF is the divisor, b, in the last equation. GCF = 4

Answer 2

Question:

Find the G.C.D. of (896,35) by Euclid's division method.

Answer:

G.C.D.(896,35) = 7

Solution:

35 ) 896 ( 25

-70

196

-175

21 ) 35 ( 1

-21

14 ) 21 ( 1

-14

7 ) 14 ( 2

-14

0

Thus, we have;

896 = 25×35 + 21

35 = 1×21 + 14

21 = 1×14 + 7

14 = 2×7 + 0

Hence,

The G.C.D.(896,35) = 7.