Question

state euclid's division lemma and hence find HCF of 16 and 28​

Answer 1

Answer:

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....

Step-by-step explanation:

Answer 2

Answer:

hcf 16= 2×2×2×2

hcf 28=2×2×7

the common factor in both is 4

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