HCF of 24, 48, 60 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 24,48,60 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(24,48,60).

Here 48 is greater than 24

Now, consider the largest number as 'a' from the given number ie., 48 and 24 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 48 > 24, we apply the division lemma to 48 and 24, to get

48 = 24 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 24 and 48 is 24

Notice that 24 = HCF(48,24) .

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

Here 60 is greater than 24

Now, consider the largest number as 'a' from the given number ie., 60 and 24 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 60 > 24, we apply the division lemma to 60 and 24, to get

60 = 24 x 2 + 12

Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 12 and 24, to get

24 = 12 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 24 and 60 is 12

Notice that 12 = HCF(24,12) = HCF(60,24) .

Therefore, HCF of 24,48,60 using Euclid's division lemma is 12.