HCF of 105, 128, 180 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 105,128,180 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(105,128,180).

Here 128 is greater than 105

Now, consider the largest number as 'a' from the given number ie., 128 and 105 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 128 > 105, we apply the division lemma to 128 and 105, to get

128 = 105 x 1 + 23

Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 23 and 105, to get

105 = 23 x 4 + 13

Step 3: We consider the new divisor 23 and the new remainder 13, and apply the division lemma to get

23 = 13 x 1 + 10

We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get

13 = 10 x 1 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 105 and 128 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(23,13) = HCF(105,23) = HCF(128,105) .

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

Here 180 is greater than 1

Now, consider the largest number as 'a' from the given number ie., 180 and 1 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 180 > 1, we apply the division lemma to 180 and 1, to get

180 = 1 x 180 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 180 is 1

Notice that 1 = HCF(180,1) .

Therefore, HCF of 105,128,180 using Euclid's division lemma is 1.