HCF of 120, 68 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 120,68 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(120,68).

Here 120 is greater than 68

Now, consider the largest number as 'a' from the given number ie., 120 and 68 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 120 > 68, we apply the division lemma to 120 and 68, to get

120 = 68 x 1 + 52

Step 2: Since the reminder 68 ≠ 0, we apply division lemma to 52 and 68, to get

68 = 52 x 1 + 16

Step 3: We consider the new divisor 52 and the new remainder 16, and apply the division lemma to get

52 = 16 x 3 + 4

We consider the new divisor 16 and the new remainder 4, and apply the division lemma to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 120 and 68 is 4

Notice that 4 = HCF(16,4) = HCF(52,16) = HCF(68,52) = HCF(120,68) .

Therefore, HCF of 120,68 using Euclid's division lemma is 4.