Use Euclid division algorithm to find …

We have to use Euclid's division algorithm to find the HCF of 210 and 55.
Given integers are 210 and 55. Clearly, 210 > 55. Applying Euclid's division lemma to 210 and 55, we get
210 = 55 {tex}\times{/tex} 3 + 45 ....(i)

Since the remainder 45 {tex}\ne{/tex} 0. So, we apply the division lemma to the divisor 55 and remainder 45 to get
55 = 45 {tex}\times{/tex} 1 + 10 ....(ii)

Since the remainder 10 {tex}\ne{/tex} 0. So, we apply division lemma to the new divisor 45 and new remainder 10 to get
45 = 10 {tex}\times{/tex} 4 + 5 ...(iii)

Since the remainder 5 {tex}\ne{/tex} 0.
We now consider the new divisor 10 and the new remainder 5, and apply division lemma to get
10 = 5 {tex}\times{/tex} 2 + 0 ...... (iv)
The remainder at this stage is zero.
Therefore, 5 is the HCF of 210 and 55.