HCF of 54, 63, 180 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 54,63,180 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(54,63,180).

Here 63 is greater than 54

Now, consider the largest number as 'a' from the given number ie., 63 and 54 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 63 > 54, we apply the division lemma to 63 and 54, to get

63 = 54 x 1 + 9

Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 9 and 54, to get

54 = 9 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 54 and 63 is 9

Notice that 9 = HCF(54,9) = HCF(63,54) .

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

Here 180 is greater than 9

Now, consider the largest number as 'a' from the given number ie., 180 and 9 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 180 > 9, we apply the division lemma to 180 and 9, to get

180 = 9 x 20 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 9 and 180 is 9

Notice that 9 = HCF(180,9) .

Therefore, HCF of 54,63,180 using Euclid's division lemma is 9.