Question

use euclid's lemma divisivion lemmma to find HCF of:-
a)156,13
b)504,980
c)1001,385
d)847,2160
e)714,135
f)270,405,315
g)377,435
h)4052,12576

Answer 1

Since 12576 > 4052

12576 = 4052 × 3 + 420

Since the remainder 420 ≠ 0

4052 = 420 × 9 + 272

Consider the new divisor 420 and the new remainder 272

420 = 272 × 1 + 148

Consider the new divisor 272 and the new remainder 148

272 = 148 × 1 + 124

Consider the new divisor 148 and the new remainder 124

148 = 124 × 1 + 24

Consider the new divisor 124 and the new remainder 24

124 = 24 × 5 + 4

Consider the new divisor 24 and the new remainder 4

24 = 4 × 6 + 0

The remainder has now become zero, so procedure stops. Since the divisor at this stage is 4, the HCF of 12576 and 4052 is 4.

Answer 2

Answer:

(a) 156 = 13*12+0

(b) 980 = 504*1+476

504 = 476*1+28

476 = 28*17+0

(c) 1001 = 385*2+231

385 = 231*1+154

231 = 154*1+77

154 = 77*2+0