HCF of 78, 156, 169 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 78,156,169 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(78,156,169).

Here 156 is greater than 78

Now, consider the largest number as 'a' from the given number ie., 156 and 78 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 156 > 78, we apply the division lemma to 156 and 78, to get

156 = 78 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 78, the HCF of 78 and 156 is 78

Notice that 78 = HCF(156,78) .

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

Here 169 is greater than 78

Now, consider the largest number as 'a' from the given number ie., 169 and 78 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 169 > 78, we apply the division lemma to 169 and 78, to get

169 = 78 x 2 + 13

Step 2: Since the reminder 78 ≠ 0, we apply division lemma to 13 and 78, to get

78 = 13 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 78 and 169 is 13

Notice that 13 = HCF(78,13) = HCF(169,78) .

Therefore, HCF of 78,156,169 using Euclid's division lemma is 13.