HCF of 108, 180, 288 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 108,180,288 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(108,180,288).

Here 180 is greater than 108

Now, consider the largest number as 'a' from the given number ie., 180 and 108 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 180 > 108, we apply the division lemma to 180 and 108, to get

180 = 108 x 1 + 72

Step 2: Since the reminder 108 ≠ 0, we apply division lemma to 72 and 108, to get

108 = 72 x 1 + 36

Step 3: We consider the new divisor 72 and the new remainder 36, and apply the division lemma to get

72 = 36 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 108 and 180 is 36

Notice that 36 = HCF(72,36) = HCF(108,72) = HCF(180,108) .

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

Here 288 is greater than 36

Now, consider the largest number as 'a' from the given number ie., 288 and 36 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 288 > 36, we apply the division lemma to 288 and 36, to get

288 = 36 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 36 and 288 is 36

Notice that 36 = HCF(288,36) .

Therefore, HCF of 108,180,288 using Euclid's division lemma is 36.