HCF of 54, 90, 108 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 54,90,108 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(54,90,108).

Here 90 is greater than 54

Now, consider the largest number as 'a' from the given number ie., 90 and 54 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 90 > 54, we apply the division lemma to 90 and 54, to get

90 = 54 x 1 + 36

Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 36 and 54, to get

54 = 36 x 1 + 18

Step 3: We consider the new divisor 36 and the new remainder 18, and apply the division lemma 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 54 and 90 is 18

Notice that 18 = HCF(36,18) = HCF(54,36) = HCF(90,54) .

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

Here 108 is greater than 18

Now, consider the largest number as 'a' from the given number ie., 108 and 18 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 108 > 18, we apply the division lemma to 108 and 18, to get

108 = 18 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 18 and 108 is 18

Notice that 18 = HCF(108,18) .

Therefore, HCF of 54,90,108 using Euclid's division lemma is 18.