Question

Find the HCF of the following pair of numbers by Euclid’s game
(i) 25 and 35
(ii) 36 and 12
(iii) 15 and 29

Answer 1

(i) HCF of (25, 35-25)
$25=5\times 5$
$10=2\times 5$
HCF of (25, 10) = 5

(ii) HCF of (36, 36 – 12)
$36=2\times 2\times 3\times 3$
$24=2\times 2\times 2\times 3$
HCF of (36, 24) $=2\times 2\times 3=12$

(iii) HCF of (15, 29 -15)
$15=3\times 5\times 1$
$14=2\times 7\times 1$
HCF of (15, 14) = 1