HCF of 7, 15, 21 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 7,15,21 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(7,15,21).

Here 15 is greater than 7

Now, consider the largest number as 'a' from the given number ie., 15 and 7 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 15 > 7, we apply the division lemma to 15 and 7, to get

15 = 7 x 2 + 1

Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 1 and 7, to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 15 is 1

Notice that 1 = HCF(7,1) = HCF(15,7) .

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

Here 21 is greater than 1

Now, consider the largest number as 'a' from the given number ie., 21 and 1 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 21 > 1, we apply the division lemma to 21 and 1, to get

21 = 1 x 21 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21 is 1

Notice that 1 = HCF(21,1) .

Therefore, HCF of 7,15,21 using Euclid's division lemma is 1.