HCF of 60, 220, 286 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 60,220,286 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(60,220,286).

Here 220 is greater than 60

Now, consider the largest number as 'a' from the given number ie., 220 and 60 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 220 > 60, we apply the division lemma to 220 and 60, to get

220 = 60 x 3 + 40

Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 40 and 60, to get

60 = 40 x 1 + 20

Step 3: We consider the new divisor 40 and the new remainder 20, and apply the division lemma to get

40 = 20 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 60 and 220 is 20

Notice that 20 = HCF(40,20) = HCF(60,40) = HCF(220,60) .

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

Here 286 is greater than 20

Now, consider the largest number as 'a' from the given number ie., 286 and 20 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 286 > 20, we apply the division lemma to 286 and 20, to get

286 = 20 x 14 + 6

Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 6 and 20, to get

20 = 6 x 3 + 2

Step 3: We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 20 and 286 is 2

Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(286,20) .

Therefore, HCF of 60,220,286 using Euclid's division lemma is 2.