HCF of 65, 99 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 65,99 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(65,99).

Here 99 is greater than 65

Now, consider the largest number as 'a' from the given number ie., 99 and 65 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 99 > 65, we apply the division lemma to 99 and 65, to get

99 = 65 x 1 + 34

Step 2: Since the reminder 65 ≠ 0, we apply division lemma to 34 and 65, to get

65 = 34 x 1 + 31

Step 3: We consider the new divisor 34 and the new remainder 31, and apply the division lemma to get

34 = 31 x 1 + 3

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

31 = 3 x 10 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 65 and 99 is 1

Notice that 1 = HCF(3,1) = HCF(31,3) = HCF(34,31) = HCF(65,34) = HCF(99,65) .

Therefore, HCF of 65,99 using Euclid's division lemma is 1.