HCF of 12, 15, 18 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 12,15,18 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(12,15,18).

Here 15 is greater than 12

Now, consider the largest number as 'a' from the given number ie., 15 and 12 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 15 > 12, we apply the division lemma to 15 and 12, to get

15 = 12 x 1 + 3

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 3 and 12, to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 12 and 15 is 3

Notice that 3 = HCF(12,3) = HCF(15,12) .

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

Here 18 is greater than 3

Now, consider the largest number as 'a' from the given number ie., 18 and 3 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 18 > 3, we apply the division lemma to 18 and 3, to get

18 = 3 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 18 is 3

Notice that 3 = HCF(18,3) .

Therefore, HCF of 12,15,18 using Euclid's division lemma is 3.