HCF of 413, 33 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 413,33 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(413,33).

Here 413 is greater than 33

Now, consider the largest number as 'a' from the given number ie., 413 and 33 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 413 > 33, we apply the division lemma to 413 and 33, to get

413 = 33 x 12 + 17

Step 2: Since the reminder 33 ≠ 0, we apply division lemma to 17 and 33, to get

33 = 17 x 1 + 16

Step 3: We consider the new divisor 17 and the new remainder 16, and apply the division lemma to get

17 = 16 x 1 + 1

We consider the new divisor 16 and the new remainder 1, and apply the division lemma to get

16 = 1 x 16 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 413 and 33 is 1

Notice that 1 = HCF(16,1) = HCF(17,16) = HCF(33,17) = HCF(413,33) .

Therefore, HCF of 413,33 using Euclid's division lemma is 1.