HCF of 12, 30, 72 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 12,30,72 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(12,30,72).

Here 30 is greater than 12

Now, consider the largest number as 'a' from the given number ie., 30 and 12 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 30 > 12, we apply the division lemma to 30 and 12, to get

30 = 12 x 2 + 6

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 6 and 12, 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 12 and 30 is 6

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

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

Here 72 is greater than 6

Now, consider the largest number as 'a' from the given number ie., 72 and 6 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 72 > 6, we apply the division lemma to 72 and 6, to get

72 = 6 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 72 is 6

Notice that 6 = HCF(72,6) .

Therefore, HCF of 12,30,72 using Euclid's division lemma is 6.