HCF of 34, 51, 85 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 34,51,85 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(34,51,85).

Here 51 is greater than 34

Now, consider the largest number as 'a' from the given number ie., 51 and 34 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 51 > 34, we apply the division lemma to 51 and 34, to get

51 = 34 x 1 + 17

Step 2: Since the reminder 34 ≠ 0, we apply division lemma to 17 and 34, to get

34 = 17 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 34 and 51 is 17

Notice that 17 = HCF(34,17) = HCF(51,34) .

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

Here 85 is greater than 17

Now, consider the largest number as 'a' from the given number ie., 85 and 17 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 85 > 17, we apply the division lemma to 85 and 17, to get

85 = 17 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 17 and 85 is 17

Notice that 17 = HCF(85,17) .

Therefore, HCF of 34,51,85 using Euclid's division lemma is 17.