How to find HCF of 690, 966, 1150 using Euclid's Algorithm?

For arbitrary numbers 690, 966, 1150 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 690, 966, 1150 using Euclid's Algorithm?

For arbitrary numbers 690, 966, 1150 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 690, 966, 1150 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 690, 966, 1150?

HCF of 690, 966, 1150 is 46 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 690, 966, 1150 ? 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 690, 966, 1150 using Euclid's algorithm i.e 46 quickly.

Detailed Method to Find the HCF of 690,966,1150 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 690,966,1150. This is how to do it.

Step 1: The first step is to use the division lemma with 966 and 690 because 966 is greater than 690

966 = 690 x 1 + 276

Step 2: Here, the reminder 690 is not 0, we must use division lemma to 276 and 690, to get

690 = 276 x 2 + 138

Step 3: We consider the new divisor 276 and the new remainder 138, and apply the division lemma to get

276 = 138 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 138.Therefore, the HCF of 690 and 966 is equal to 138

Notice that 138 = HCF(276,138) = HCF(690,276) = HCF(966,690) .

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 1150 and 138 because 1150 is greater than 138

1150 = 138 x 8 + 46

Step 2: Here, the reminder 138 is not 0, we must use division lemma to 46 and 138, to get

138 = 46 x 3 + 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 46.Therefore, the HCF of 138 and 1150 is equal to 46

Notice that 46 = HCF(138,46) = HCF(1150,138) .

Result

Hence, the HCF of 690, 966, 1150 is equal to 46.

FAQ on HCF of 690, 966, 1150 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 690, 966, 1150?

Answer: The HCF of 690, 966, 1150 is 46.