HCF of 120, 150, 135 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 120,150,135 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(120,150,135).

Here 150 is greater than 120

Now, consider the largest number as 'a' from the given number ie., 150 and 120 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 150 > 120, we apply the division lemma to 150 and 120, to get

150 = 120 x 1 + 30

Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 30 and 120, to get

120 = 30 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 120 and 150 is 30

Notice that 30 = HCF(120,30) = HCF(150,120) .

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

Here 135 is greater than 30

Now, consider the largest number as 'a' from the given number ie., 135 and 30 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 135 > 30, we apply the division lemma to 135 and 30, to get

135 = 30 x 4 + 15

Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 15 and 30, to get

30 = 15 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 30 and 135 is 15

Notice that 15 = HCF(30,15) = HCF(135,30) .

Therefore, HCF of 120,150,135 using Euclid's division lemma is 15.