How to find HCF of 162, 405, 927, 900 using Euclid's Algorithm?

For arbitrary numbers 162, 405, 927, 900 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 162, 405, 927, 900 using Euclid's Algorithm?

For arbitrary numbers 162, 405, 927, 900 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 162, 405, 927, 900 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 162, 405, 927, 900?

HCF of 162, 405, 927, 900 is 9 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 162, 405, 927, 900 ? 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 162, 405, 927, 900 using Euclid's algorithm i.e 9 quickly.

Detailed Method to Find the HCF of 162,405,927,900 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 162,405,927,900. This is how to do it.

Step 1: The first step is to use the division lemma with 405 and 162 because 405 is greater than 162

405 = 162 x 2 + 81

Step 2: Here, the reminder 162 is not 0, we must use division lemma to 81 and 162, to get

162 = 81 x 2 + 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 81.Therefore, the HCF of 162 and 405 is equal to 81

Notice that 81 = HCF(162,81) = HCF(405,162) .

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 927 and 81 because 927 is greater than 81

927 = 81 x 11 + 36

Step 2: Here, the reminder 81 is not 0, we must use division lemma to 36 and 81, to get

81 = 36 x 2 + 9

Step 3: We consider the new divisor 36 and the new remainder 9, and apply the division lemma to get

36 = 9 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 9.Therefore, the HCF of 81 and 927 is equal to 9

Notice that 9 = HCF(36,9) = HCF(81,36) = HCF(927,81) .

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 900 and 9 because 900 is greater than 9

900 = 9 x 100 + 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 9.Therefore, the HCF of 9 and 900 is equal to 9

Notice that 9 = HCF(900,9) .

Result

Hence, the HCF of 162, 405, 927, 900 is equal to 9.

FAQ on HCF of 162, 405, 927, 900 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 162, 405, 927, 900?

Answer: The HCF of 162, 405, 927, 900 is 9.