HCF of 12, 20, 28 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 12,20,28 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(12,20,28).

Here 20 is greater than 12

Now, consider the largest number as 'a' from the given number ie., 20 and 12 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 20 > 12, we apply the division lemma to 20 and 12, to get

20 = 12 x 1 + 8

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 8 and 12, to get

12 = 8 x 1 + 4

Step 3: We consider the new divisor 8 and the new remainder 4, and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 12 and 20 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) .

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

Here 28 is greater than 4

Now, consider the largest number as 'a' from the given number ie., 28 and 4 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 28 > 4, we apply the division lemma to 28 and 4, to get

28 = 4 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 28 is 4

Notice that 4 = HCF(28,4) .

Therefore, HCF of 12,20,28 using Euclid's division lemma is 4.