HCF of 18, 24, 60 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 18,24,60 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(18,24,60).

Here 24 is greater than 18

Now, consider the largest number as 'a' from the given number ie., 24 and 18 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 24 > 18, we apply the division lemma to 24 and 18, to get

24 = 18 x 1 + 6

Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 6 and 18, to get

18 = 6 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 18 and 24 is 6

Notice that 6 = HCF(18,6) = HCF(24,18) .

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

Here 60 is greater than 6

Now, consider the largest number as 'a' from the given number ie., 60 and 6 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 60 > 6, we apply the division lemma to 60 and 6, to get

60 = 6 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 60 is 6

Notice that 6 = HCF(60,6) .

Therefore, HCF of 18,24,60 using Euclid's division lemma is 6.