How to find HCF of 200, 445, 145 using Euclid's Algorithm?

For arbitrary numbers 200, 445, 145 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.

How to find HCF of 200, 445, 145 using Euclid's Algorithm?

For arbitrary numbers 200, 445, 145 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.

HCF of 200, 445, 145 using Euclid's algorithm

Q: What is the Euclid division algorithm?

Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

Q: what is the HCF of 200, 445, 145?

HCF of 200, 445, 145 is 5 the largest number that divides all the numbers leaving a remainder zero.

Created By : Jatin Gogia
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023

Want to know how to use Euclid’s algorithm to find the HCF of 200, 445, 145 ? Well, you have come to the right place. In this article, you will be learning about Euclid’s algorithm and how to use it to calculate the HCF with ease.
Take the help of the HCF Calculator using the Euclid Division Algorithm which finds HCF of 200, 445, 145 using Euclid's algorithm i.e 5 quickly.

Detailed Method to Find the HCF of 200,445,145 using Euclid's algorithm

Euclid’s algorithm is written as a = bq + r. This is known as the division lemma. The variable r varies according to 0 ≤ r ≤ b. We can use this to figure out the HCF of 200,445,145. This is how to do it.

Step 1: The first step is to use the division lemma with 445 and 200 because 445 is greater than 200

445 = 200 x 2 + 45

Step 2: Here, the reminder 200 is not 0, we must use division lemma to 45 and 200, to get

200 = 45 x 4 + 20

Step 3: We consider the new divisor 45 and the new remainder 20, and apply the division lemma to get

45 = 20 x 2 + 5

We consider the new divisor 20 and the new remainder 5, and apply the division lemma to get

20 = 5 x 4 + 0

As you can see, the remainder is zero, so you may end the process at this point. From the last equation, we can determine that the divisor is 5.Therefore, the HCF of 200 and 445 is equal to 5

Notice that 5 = HCF(20,5) = HCF(45,20) = HCF(200,45) = HCF(445,200) .

Now, we must treat the HCF of the first two numbers as the next number in our calculation, and next

Step 1: The first step is to use the division lemma with 145 and 5 because 145 is greater than 5

145 = 5 x 29 + 0

As you can see, the remainder is zero, so you may end the process at this point. From the last equation, we can determine that the divisor is 5.Therefore, the HCF of 5 and 145 is equal to 5

Notice that 5 = HCF(145,5) .

Result

Hence, the HCF of 200, 445, 145 is equal to 5.

FAQ on HCF of 200, 445, 145 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid’s algorithm is represented as a = bq + r, and 0 ≤ r ≤ b..

2. How do you find HCF using Euclid's algorithm ?

Answer: Apply the division lemma to the numbers, and keep going until the remainder is zero. Once it becomes zero, the divisor will be your HCF.

3. What is the HCF of 200, 445, 145?

Answer: The HCF of 200, 445, 145 is 5.