HCF of 234, 91 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 234,91 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(234,91).

Here 234 is greater than 91

Now, consider the largest number as 'a' from the given number ie., 234 and 91 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 234 > 91, we apply the division lemma to 234 and 91, to get

234 = 91 x 2 + 52

Step 2: Since the reminder 91 ≠ 0, we apply division lemma to 52 and 91, to get

91 = 52 x 1 + 39

Step 3: We consider the new divisor 52 and the new remainder 39, and apply the division lemma to get

52 = 39 x 1 + 13

We consider the new divisor 39 and the new remainder 13, and apply the division lemma to get

39 = 13 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 234 and 91 is 13

Notice that 13 = HCF(39,13) = HCF(52,39) = HCF(91,52) = HCF(234,91) .

Therefore, HCF of 234,91 using Euclid's division lemma is 13.