HCF of 18, 30, 54 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 18,30,54 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(18,30,54).

Here 30 is greater than 18

Now, consider the largest number as 'a' from the given number ie., 30 and 18 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 30 > 18, we apply the division lemma to 30 and 18, to get

30 = 18 x 1 + 12

Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 12 and 18, to get

18 = 12 x 1 + 6

Step 3: We consider the new divisor 12 and the new remainder 6, and apply the division lemma to get

12 = 6 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 18 and 30 is 6

Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) .

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

Here 54 is greater than 6

Now, consider the largest number as 'a' from the given number ie., 54 and 6 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 54 > 6, we apply the division lemma to 54 and 6, to get

54 = 6 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 54 is 6

Notice that 6 = HCF(54,6) .

Therefore, HCF of 18,30,54 using Euclid's division lemma is 6.