HCF of 45, 60, 120 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 45,60,120 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(45,60,120).

Here 60 is greater than 45

Now, consider the largest number as 'a' from the given number ie., 60 and 45 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 60 > 45, we apply the division lemma to 60 and 45, to get

60 = 45 x 1 + 15

Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 15 and 45, to get

45 = 15 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 45 and 60 is 15

Notice that 15 = HCF(45,15) = HCF(60,45) .

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

Here 120 is greater than 15

Now, consider the largest number as 'a' from the given number ie., 120 and 15 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 120 > 15, we apply the division lemma to 120 and 15, to get

120 = 15 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 15 and 120 is 15

Notice that 15 = HCF(120,15) .

Therefore, HCF of 45,60,120 using Euclid's division lemma is 15.