Question

2015 and 1860 division algorithm by euclid

Answer 1

Answer:

• The divisor at this stage, ie, 155 is the HCF of 2015 and 1860.

Given :

• The numbers = 2015 and 1860.

To find :

• The HCF of 2015 and 1860 =?

Step-by-step explanation:

Euclid's division lemma:

Given positive numbers a and b ,

There exist whole numbers q and r

satisfying ,

a = bq + r ,

0 ≤ r < b

Clearly 2015 > 1860

Applying Euclid's division lemma to 2015 and 1860, we get

2015 = 1860 × 1 + 155

Since the remainder 155 ≠ 0 , we apply the Euclid's division lemma to divisor 1860 and remainder 155 to get

1860 = 155 × 12 + 0

Now, the remainder at this stage is 0.

So, the divisor at this stage, ie, 155 is the HCF of 2015 and 1860.