Question

using euclid's division algorithm find whether the HCF of 2160 and 3520

Answer 1

The HCF OF 2160 & 3520 IS 80.

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Answer 2

Euclid's division algorithm:

According to this the HCF of any two positive integers a and b, with a>b

a= bq+r, 0 ≤r
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a= 3520 , b= 2160

On applying euclid's division Lemma for 2160 & 3520

3520 = (2160×1)+1360

Here, remainder= 1360≠0
So take new Dividend as 2160 & divisior as 1360

2160 = (1360×1)+800


Here, remainder= 800≠0
So take new Dividend as 1360 & divisior as 800

1360= (800×1)+560


Here, remainder= 560≠0
So take new Dividend as 800 & divisior as 560

800 = (560×1)+240


Here, remainder= 240≠0
So take new Dividend as 560 & divisior as 240

560 = (240×2)+80


Here, remainder= 80≠0
So take new Dividend as 240 & divisior as 80

240 = (80×3)+0

Here, the remainder is 0 & last divisor is 80.

Hence , HCF of 2160 & 3520 is 80

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