Question

Through Euclid algorithm find HCF of 12 ,14,16

Answer 1

by Euclid's division algorithm,
14=12×1+2
12=2×6+0
HCF of 14,12=2
16=2×8+0
HCF of 12,14,16=2.

Answer 2

Euclid's division algorithm is a technique to compute the Highest Common Factor (HCF) of two or three given positive integers.

Euclid's division Lemma states that for any two positive integers say a and b there exist two unique whole numbers say q and r ,such that, a = bq+r, where 0≤r<b.

SOLUTION:

FOR 12,14 and 16

12=2×2×3
14=2×7
16=2×2×2×2

Since 2 is common in all of the above prime factors, HCF=2.