HCF of 54, 72, 198 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 54,72,198 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(54,72,198).

Here 72 is greater than 54

Now, consider the largest number as 'a' from the given number ie., 72 and 54 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 72 > 54, we apply the division lemma to 72 and 54, to get

72 = 54 x 1 + 18

Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 18 and 54, to get

54 = 18 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 54 and 72 is 18

Notice that 18 = HCF(54,18) = HCF(72,54) .

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

Here 198 is greater than 18

Now, consider the largest number as 'a' from the given number ie., 198 and 18 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 198 > 18, we apply the division lemma to 198 and 18, to get

198 = 18 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 18 and 198 is 18

Notice that 18 = HCF(198,18) .

Therefore, HCF of 54,72,198 using Euclid's division lemma is 18.