HCF of 135, 180, 225 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 135,180,225 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(135,180,225).

Here 180 is greater than 135

Now, consider the largest number as 'a' from the given number ie., 180 and 135 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 180 > 135, we apply the division lemma to 180 and 135, to get

180 = 135 x 1 + 45

Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 45 and 135, to get

135 = 45 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 135 and 180 is 45

Notice that 45 = HCF(135,45) = HCF(180,135) .

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

Here 225 is greater than 45

Now, consider the largest number as 'a' from the given number ie., 225 and 45 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 225 > 45, we apply the division lemma to 225 and 45, to get

225 = 45 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 45 and 225 is 45

Notice that 45 = HCF(225,45) .

Therefore, HCF of 135,180,225 using Euclid's division lemma is 45.