HCF of 91, 75 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 91,75 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(91,75).

Here 91 is greater than 75

Now, consider the largest number as 'a' from the given number ie., 91 and 75 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 91 > 75, we apply the division lemma to 91 and 75, to get

91 = 75 x 1 + 16

Step 2: Since the reminder 75 ≠ 0, we apply division lemma to 16 and 75, to get

75 = 16 x 4 + 11

Step 3: We consider the new divisor 16 and the new remainder 11, and apply the division lemma to get

16 = 11 x 1 + 5

We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get

11 = 5 x 2 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 91 and 75 is 1

Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(75,16) = HCF(91,75) .

Therefore, HCF of 91,75 using Euclid's division lemma is 1.