HCF of 110, 68 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 110,68 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(110,68).

Here 110 is greater than 68

Now, consider the largest number as 'a' from the given number ie., 110 and 68 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 110 > 68, we apply the division lemma to 110 and 68, to get

110 = 68 x 1 + 42

Step 2: Since the reminder 68 ≠ 0, we apply division lemma to 42 and 68, to get

68 = 42 x 1 + 26

Step 3: We consider the new divisor 42 and the new remainder 26, and apply the division lemma to get

42 = 26 x 1 + 16

We consider the new divisor 26 and the new remainder 16,and apply the division lemma to get

26 = 16 x 1 + 10

We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get

16 = 10 x 1 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 110 and 68 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(26,16) = HCF(42,26) = HCF(68,42) = HCF(110,68) .

Therefore, HCF of 110,68 using Euclid's division lemma is 2.