Question

Use Euclid’s division algorithm to find the HCF of 16 and 28.

Answer 1

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:
On applying euclid's division Lemma for 16 and 28

28 = 16 ×1 + 12
Here, Remainder = 12≠0
So take new Dividend as 16 and divisor as 12.

16 = 12×1 +4
Here, Remainder = 14≠0
So take new Dividend as 12 and divisor as 4.

12 = 4×3 +0
Here, the Remainder = 0 and the last divisor is 4.
Hence, HCF of 16 and 28 is 4.

HOPE THIS WILL HELP YOU....

Answer 2

28 = 16 x 1 + 12

16 = 12 x 1 + 4

12 = 4x 3 + 0


hence , the HCF is 4;

hope it helps!!!

thanks