HCF of 65, 143, 169 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 65,143,169 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(65,143,169).

Here 143 is greater than 65

Now, consider the largest number as 'a' from the given number ie., 143 and 65 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 143 > 65, we apply the division lemma to 143 and 65, to get

143 = 65 x 2 + 13

Step 2: Since the reminder 65 ≠ 0, we apply division lemma to 13 and 65, to get

65 = 13 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 65 and 143 is 13

Notice that 13 = HCF(65,13) = HCF(143,65) .

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

Here 169 is greater than 13

Now, consider the largest number as 'a' from the given number ie., 169 and 13 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 169 > 13, we apply the division lemma to 169 and 13, to get

169 = 13 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 13 and 169 is 13

Notice that 13 = HCF(169,13) .

Therefore, HCF of 65,143,169 using Euclid's division lemma is 13.