Question

Using euclid algorithm to find the hcf of 196 and 38220

Answer 1

First of all we'll need to know what is Euclid's Algorithm, or Euclidean algorithm. It is an algorithm for finding the Highest Common Factor (HCF) of two numbers a and b using Euclid's Division Lemma.

To obtain the HCF of two prime positive integers a and b with a > b, follow the steps below:

• Step 1: Apply Euclid's Division Lemma to a and b such that we find whole numbers q and r, $a = bq + r, 0 \leq r < d$
• Step 2: If r = 0, b is the HCF of a and b. If r  not equal to 0 apply division Lemma to b and r.
• Step 3: Continue the process till the remainder is 0.  

The divisor at this stage will be the required HCF.

So, Now Let's get into the question;

So, According to the question the value of a = 38220 and b = 196

**See I took the value of a as 38220 instead of 196 because as we already said a should be greater than b and the value of 196 is less than that of the value of 38220**

So, Now we have all the values; So let's plug them in and start the question;

$38220 = 196 \times 195 + 0$

Here, we got the value of r as 0, so, we can say 196 is the HCF of 196 and 38220.

Answer 2

Answer:

196 and 38220

We have 38220 > 196,

So, we apply the division lemma to 38220 and 196 to obtain

38220 = 196 × 195 + 0

Since we get the remainder as zero, the process stops.

The divisor at this stage is 196,

Therefore, HCF of 196 and 38220 is 196.

Step-by-step explanation:

Hope this helps you ✌️