HCF of 13, 39, 23 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 13,39,23 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(13,39,23).

Here 39 is greater than 13

Now, consider the largest number as 'a' from the given number ie., 39 and 13 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 39 > 13, we apply the division lemma to 39 and 13, to get

39 = 13 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 13 and 39 is 13

Notice that 13 = HCF(39,13) .

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

Here 23 is greater than 13

Now, consider the largest number as 'a' from the given number ie., 23 and 13 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 23 > 13, we apply the division lemma to 23 and 13, to get

23 = 13 x 1 + 10

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 10 and 13, to get

13 = 10 x 1 + 3

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

10 = 3 x 3 + 1

We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 23 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(23,13) .

Therefore, HCF of 13,39,23 using Euclid's division lemma is 1.