HCF of 25, 35, 45 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 25,35,45 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(25,35,45).

Here 35 is greater than 25

Now, consider the largest number as 'a' from the given number ie., 35 and 25 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 35 > 25, we apply the division lemma to 35 and 25, to get

35 = 25 x 1 + 10

Step 2: Since the reminder 25 ≠ 0, we apply division lemma to 10 and 25, to get

25 = 10 x 2 + 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 25 and 35 is 5

Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(35,25) .

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

Here 45 is greater than 5

Now, consider the largest number as 'a' from the given number ie., 45 and 5 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 45 > 5, we apply the division lemma to 45 and 5, to get

45 = 5 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 45 is 5

Notice that 5 = HCF(45,5) .

Therefore, HCF of 25,35,45 using Euclid's division lemma is 5.