Question

using Euclid division algorithm, find the HCF of 2160 and 3520​

Answer 1

★We know that for finding the HCF of two distinct positive integers a and b ( a > b ) and we obtain two integers q and r such that

a = b × q + r , 0 ≤ r < b

Step 1 :

2160) 3520 ( 1

2160

----------------

1360

3620 = 2160 × 1 + 1360

Step 2 :

Remainder obtained in step ( 1 ) is 1360 which is not zero.So, now will take 1360 as divisor and 2160 as dividend.

1360) 2160 ( 1

1360

-----------

800

2160 = 1360 × 1 + 800

Step 3 :

Remainder obtained in step ( 2 ) is 800 which is not zero.Hence , now 800 will taken as divisor and 1360 as dividend.

800) 1360 ( 1

800

------------

560

1360 = 800 × 1 + 560

Step 4 :

Remainder obtained in step ( 3 ) is 560 which is not zero. So, now will take 560 as divisor and 800 as dividend.

560) 800 ( 1

560

---------

240

800 = 560 × 1 + 240

Step 5 :

Remainder obtained in step ( 4 ) is 240 which is not zero. Now, we consider the divisor 560 as dividend and the remainder 240 as divisor.

240) 560 ( 2

480

----------

80

560 = 240 × 2 + 80

Step 6 :

Remainder obtained in step ( 5 ) is 80 which is not zero. Now, consider the divisor 240 as dividend and the remainder 80 as divisor by division algorithm.

80) 240 ( 3

240

------------

0

240 = 80 × 3 + 0

Finally, we get remainder as zero .

Hence, HCF of ( 2160, 3520 ) is 80 because last divisor in solving this problem is 80 .