HCF of 51, 85, 153 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 51,85,153 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(51,85,153).

Here 85 is greater than 51

Now, consider the largest number as 'a' from the given number ie., 85 and 51 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 85 > 51, we apply the division lemma to 85 and 51, to get

85 = 51 x 1 + 34

Step 2: Since the reminder 51 ≠ 0, we apply division lemma to 34 and 51, to get

51 = 34 x 1 + 17

Step 3: We consider the new divisor 34 and the new remainder 17, and apply the division lemma 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 51 and 85 is 17

Notice that 17 = HCF(34,17) = HCF(51,34) = HCF(85,51) .

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

Here 153 is greater than 17

Now, consider the largest number as 'a' from the given number ie., 153 and 17 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 153 > 17, we apply the division lemma to 153 and 17, to get

153 = 17 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 17 and 153 is 17

Notice that 17 = HCF(153,17) .

Therefore, HCF of 51,85,153 using Euclid's division lemma is 17.