Question

Find the $HCF$ of $25$ and $140$ using Euclid division algorithum.

Answer 1

Given integers are 25 and 140. clearly,140>25. applying euclid's division lemma to 140 and 25,we get

$140=25\times 5+15$

Since the remainder $15\ne 0$. so,we apply the division lemma to the divisor 25and remainder 15 to get

$25=15\times 1+10$

Now, we apply division lemma to the new divisor 15 and new remainder 10 to get

$15=10\times 1+5$

We know consider the new divisor 10 and the new remainder 5,and apply division lemma to get

$10=5\times 2+0$

The remainder at this stage is zero . so the divisor at this atage or the remainder at the previous stage i.e,5 is the HCF of 140 and 25.