HCF of 20, 85, 120 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 20,85,120 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(20,85,120).

Here 85 is greater than 20

Now, consider the largest number as 'a' from the given number ie., 85 and 20 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 85 > 20, we apply the division lemma to 85 and 20, to get

85 = 20 x 4 + 5

Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 5 and 20, to get

20 = 5 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 20 and 85 is 5

Notice that 5 = HCF(20,5) = HCF(85,20) .

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

Here 120 is greater than 5

Now, consider the largest number as 'a' from the given number ie., 120 and 5 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 120 > 5, we apply the division lemma to 120 and 5, to get

120 = 5 x 24 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 120 is 5

Notice that 5 = HCF(120,5) .

Therefore, HCF of 20,85,120 using Euclid's division lemma is 5.