HCF of 9, 156, 169 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 9,156,169 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(9,156,169).

Here 156 is greater than 9

Now, consider the largest number as 'a' from the given number ie., 156 and 9 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 156 > 9, we apply the division lemma to 156 and 9, to get

156 = 9 x 17 + 3

Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 3 and 9, to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9 and 156 is 3

Notice that 3 = HCF(9,3) = HCF(156,9) .

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

Here 169 is greater than 3

Now, consider the largest number as 'a' from the given number ie., 169 and 3 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 169 > 3, we apply the division lemma to 169 and 3, to get

169 = 3 x 56 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 169 is 1

Notice that 1 = HCF(3,1) = HCF(169,3) .

Therefore, HCF of 9,156,169 using Euclid's division lemma is 1.