HCF of 110, 46 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 110,46 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(110,46).

Here 110 is greater than 46

Now, consider the largest number as 'a' from the given number ie., 110 and 46 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 110 > 46, we apply the division lemma to 110 and 46, to get

110 = 46 x 2 + 18

Step 2: Since the reminder 46 ≠ 0, we apply division lemma to 18 and 46, to get

46 = 18 x 2 + 10

Step 3: We consider the new divisor 18 and the new remainder 10, and apply the division lemma to get

18 = 10 x 1 + 8

We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get

10 = 8 x 1 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 110 and 46 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(46,18) = HCF(110,46) .

Therefore, HCF of 110,46 using Euclid's division lemma is 2.