HCF of 68, 377, 116 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 68,377,116 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(68,377,116).

Here 377 is greater than 68

Now, consider the largest number as 'a' from the given number ie., 377 and 68 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 377 > 68, we apply the division lemma to 377 and 68, to get

377 = 68 x 5 + 37

Step 2: Since the reminder 68 ≠ 0, we apply division lemma to 37 and 68, to get

68 = 37 x 1 + 31

Step 3: We consider the new divisor 37 and the new remainder 31, and apply the division lemma to get

37 = 31 x 1 + 6

We consider the new divisor 31 and the new remainder 6,and apply the division lemma to get

31 = 6 x 5 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 68 and 377 is 1

Notice that 1 = HCF(6,1) = HCF(31,6) = HCF(37,31) = HCF(68,37) = HCF(377,68) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Here 116 is greater than 1

Now, consider the largest number as 'a' from the given number ie., 116 and 1 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 116 > 1, we apply the division lemma to 116 and 1, to get

116 = 1 x 116 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 116 is 1

Notice that 1 = HCF(116,1) .

Therefore, HCF of 68,377,116 using Euclid's division lemma is 1.