HCF of 30, 48, 60, 66 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 30,48,60,66 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(30,48,60,66).

Here 48 is greater than 30

Now, consider the largest number as 'a' from the given number ie., 48 and 30 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 48 > 30, we apply the division lemma to 48 and 30, to get

48 = 30 x 1 + 18

Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 18 and 30, to get

30 = 18 x 1 + 12

Step 3: We consider the new divisor 18 and the new remainder 12, and apply the division lemma to get

18 = 12 x 1 + 6

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 30 and 48 is 6

Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(48,30) .

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

Here 60 is greater than 6

Now, consider the largest number as 'a' from the given number ie., 60 and 6 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 60 > 6, we apply the division lemma to 60 and 6, to get

60 = 6 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 60 is 6

Notice that 6 = HCF(60,6) .

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

Here 66 is greater than 6

Now, consider the largest number as 'a' from the given number ie., 66 and 6 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 66 > 6, we apply the division lemma to 66 and 6, to get

66 = 6 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 66 is 6

Notice that 6 = HCF(66,6) .

Therefore, HCF of 30,48,60,66 using Euclid's division lemma is 6.