HCF of 45, 63, 81 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 45,63,81 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(45,63,81).

Here 63 is greater than 45

Now, consider the largest number as 'a' from the given number ie., 63 and 45 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 63 > 45, we apply the division lemma to 63 and 45, to get

63 = 45 x 1 + 18

Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 18 and 45, to get

45 = 18 x 2 + 9

Step 3: We consider the new divisor 18 and the new remainder 9, and apply the division lemma to get

18 = 9 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 45 and 63 is 9

Notice that 9 = HCF(18,9) = HCF(45,18) = HCF(63,45) .

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

Here 81 is greater than 9

Now, consider the largest number as 'a' from the given number ie., 81 and 9 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 81 > 9, we apply the division lemma to 81 and 9, to get

81 = 9 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 9 and 81 is 9

Notice that 9 = HCF(81,9) .

Therefore, HCF of 45,63,81 using Euclid's division lemma is 9.