HCF of 108, 120, 144 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 108,120,144 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(108,120,144).

Here 120 is greater than 108

Now, consider the largest number as 'a' from the given number ie., 120 and 108 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 120 > 108, we apply the division lemma to 120 and 108, to get

120 = 108 x 1 + 12

Step 2: Since the reminder 108 ≠ 0, we apply division lemma to 12 and 108, to get

108 = 12 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 108 and 120 is 12

Notice that 12 = HCF(108,12) = HCF(120,108) .

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

Here 144 is greater than 12

Now, consider the largest number as 'a' from the given number ie., 144 and 12 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 144 > 12, we apply the division lemma to 144 and 12, to get

144 = 12 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 12 and 144 is 12

Notice that 12 = HCF(144,12) .

Therefore, HCF of 108,120,144 using Euclid's division lemma is 12.