HCF of 27, 96, 682 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 27,96,682 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(27,96,682).

Here 96 is greater than 27

Now, consider the largest number as 'a' from the given number ie., 96 and 27 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 96 > 27, we apply the division lemma to 96 and 27, to get

96 = 27 x 3 + 15

Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 15 and 27, to get

27 = 15 x 1 + 12

Step 3: We consider the new divisor 15 and the new remainder 12, and apply the division lemma to get

15 = 12 x 1 + 3

We consider the new divisor 12 and the new remainder 3, and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 27 and 96 is 3

Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(96,27) .

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

Here 682 is greater than 3

Now, consider the largest number as 'a' from the given number ie., 682 and 3 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 682 > 3, we apply the division lemma to 682 and 3, to get

682 = 3 x 227 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 682 is 1

Notice that 1 = HCF(3,1) = HCF(682,3) .

Therefore, HCF of 27,96,682 using Euclid's division lemma is 1.