HCF of 36, 45, 60 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 36,45,60 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(36,45,60).

Here 45 is greater than 36

Now, consider the largest number as 'a' from the given number ie., 45 and 36 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 45 > 36, we apply the division lemma to 45 and 36, to get

45 = 36 x 1 + 9

Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 9 and 36, to get

36 = 9 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 36 and 45 is 9

Notice that 9 = HCF(36,9) = HCF(45,36) .

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

Here 60 is greater than 9

Now, consider the largest number as 'a' from the given number ie., 60 and 9 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 60 > 9, we apply the division lemma to 60 and 9, to get

60 = 9 x 6 + 6

Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 6 and 9, to get

9 = 6 x 1 + 3

Step 3: We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9 and 60 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(60,9) .

Therefore, HCF of 36,45,60 using Euclid's division lemma is 3.