HCF of 36, 48, 72 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 36,48,72 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(36,48,72).

Here 48 is greater than 36

Now, consider the largest number as 'a' from the given number ie., 48 and 36 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 48 > 36, we apply the division lemma to 48 and 36, to get

48 = 36 x 1 + 12

Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 12 and 36, to get

36 = 12 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 36 and 48 is 12

Notice that 12 = HCF(36,12) = HCF(48,36) .

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

Here 72 is greater than 12

Now, consider the largest number as 'a' from the given number ie., 72 and 12 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 72 > 12, we apply the division lemma to 72 and 12, to get

72 = 12 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 12 and 72 is 12

Notice that 12 = HCF(72,12) .

Therefore, HCF of 36,48,72 using Euclid's division lemma is 12.