HCF of 20, 50, 100 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 20,50,100 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(20,50,100).

Here 50 is greater than 20

Now, consider the largest number as 'a' from the given number ie., 50 and 20 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 50 > 20, we apply the division lemma to 50 and 20, to get

50 = 20 x 2 + 10

Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 10 and 20, to get

20 = 10 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 20 and 50 is 10

Notice that 10 = HCF(20,10) = HCF(50,20) .

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

Here 100 is greater than 10

Now, consider the largest number as 'a' from the given number ie., 100 and 10 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 100 > 10, we apply the division lemma to 100 and 10, to get

100 = 10 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 10 and 100 is 10

Notice that 10 = HCF(100,10) .

Therefore, HCF of 20,50,100 using Euclid's division lemma is 10.