HCF of 36, 48, 60, 108 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 36,48,60,108 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(36,48,60,108).

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 60 is greater than 12

Now, consider the largest number as 'a' from the given number ie., 60 and 12 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 60 > 12, we apply the division lemma to 60 and 12, to get

60 = 12 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 12 and 60 is 12

Notice that 12 = HCF(60,12) .

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

Here 108 is greater than 12

Now, consider the largest number as 'a' from the given number ie., 108 and 12 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 108 > 12, we apply the division lemma to 108 and 12, to get

108 = 12 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 12 and 108 is 12

Notice that 12 = HCF(108,12) .

Therefore, HCF of 36,48,60,108 using Euclid's division lemma is 12.