HCF of 81, 93, 360 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 81,93,360 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(81,93,360).

Here 93 is greater than 81

Now, consider the largest number as 'a' from the given number ie., 93 and 81 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 93 > 81, we apply the division lemma to 93 and 81, to get

93 = 81 x 1 + 12

Step 2: Since the reminder 81 ≠ 0, we apply division lemma to 12 and 81, to get

81 = 12 x 6 + 9

Step 3: We consider the new divisor 12 and the new remainder 9, and apply the division lemma to get

12 = 9 x 1 + 3

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

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 81 and 93 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(81,12) = HCF(93,81) .

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

Here 360 is greater than 3

Now, consider the largest number as 'a' from the given number ie., 360 and 3 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 360 > 3, we apply the division lemma to 360 and 3, to get

360 = 3 x 120 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 360 is 3

Notice that 3 = HCF(360,3) .

Therefore, HCF of 81,93,360 using Euclid's division lemma is 3.