HCF of 36, 54, 135 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 36,54,135 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(36,54,135).

Here 54 is greater than 36

Now, consider the largest number as 'a' from the given number ie., 54 and 36 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 54 > 36, we apply the division lemma to 54 and 36, to get

54 = 36 x 1 + 18

Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 18 and 36, to get

36 = 18 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 36 and 54 is 18

Notice that 18 = HCF(36,18) = HCF(54,36) .

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

Here 135 is greater than 18

Now, consider the largest number as 'a' from the given number ie., 135 and 18 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 135 > 18, we apply the division lemma to 135 and 18, to get

135 = 18 x 7 + 9

Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 9 and 18, to get

18 = 9 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 18 and 135 is 9

Notice that 9 = HCF(18,9) = HCF(135,18) .

Therefore, HCF of 36,54,135 using Euclid's division lemma is 9.