HCF of 48, 60, 85 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 48,60,85 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(48,60,85).

Here 60 is greater than 48

Now, consider the largest number as 'a' from the given number ie., 60 and 48 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 60 > 48, we apply the division lemma to 60 and 48, to get

60 = 48 x 1 + 12

Step 2: Since the reminder 48 ≠ 0, we apply division lemma to 12 and 48, to get

48 = 12 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 48 and 60 is 12

Notice that 12 = HCF(48,12) = HCF(60,48) .

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

Here 85 is greater than 12

Now, consider the largest number as 'a' from the given number ie., 85 and 12 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 85 > 12, we apply the division lemma to 85 and 12, to get

85 = 12 x 7 + 1

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 1 and 12, to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 12 and 85 is 1

Notice that 1 = HCF(12,1) = HCF(85,12) .

Therefore, HCF of 48,60,85 using Euclid's division lemma is 1.