HCF of 15, 25, 30 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 15,25,30 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(15,25,30).

Here 25 is greater than 15

Now, consider the largest number as 'a' from the given number ie., 25 and 15 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 25 > 15, we apply the division lemma to 25 and 15, to get

25 = 15 x 1 + 10

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 10 and 15, to get

15 = 10 x 1 + 5

Step 3: We consider the new divisor 10 and the new remainder 5, and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 15 and 25 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) .

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

Here 30 is greater than 5

Now, consider the largest number as 'a' from the given number ie., 30 and 5 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 30 > 5, we apply the division lemma to 30 and 5, to get

30 = 5 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 30 is 5

Notice that 5 = HCF(30,5) .

Therefore, HCF of 15,25,30 using Euclid's division lemma is 5.