HCF of 89, 25 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 89,25 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(89,25).

Here 89 is greater than 25

Now, consider the largest number as 'a' from the given number ie., 89 and 25 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 89 > 25, we apply the division lemma to 89 and 25, to get

89 = 25 x 3 + 14

Step 2: Since the reminder 25 ≠ 0, we apply division lemma to 14 and 25, to get

25 = 14 x 1 + 11

Step 3: We consider the new divisor 14 and the new remainder 11, and apply the division lemma to get

14 = 11 x 1 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 89 and 25 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(25,14) = HCF(89,25) .

Therefore, HCF of 89,25 using Euclid's division lemma is 1.