HCF of 15, 18, 16 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 15,18,16 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(15,18,16).

Here 18 is greater than 15

Now, consider the largest number as 'a' from the given number ie., 18 and 15 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 18 > 15, we apply the division lemma to 18 and 15, to get

18 = 15 x 1 + 3

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 3 and 15, to get

15 = 3 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 15 and 18 is 3

Notice that 3 = HCF(15,3) = HCF(18,15) .

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

Here 16 is greater than 3

Now, consider the largest number as 'a' from the given number ie., 16 and 3 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 16 > 3, we apply the division lemma to 16 and 3, to get

16 = 3 x 5 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 16 is 1

Notice that 1 = HCF(3,1) = HCF(16,3) .

Therefore, HCF of 15,18,16 using Euclid's division lemma is 1.