How to find HCF of 920, 520, 670 using Euclid's Algorithm?

For arbitrary numbers 920, 520, 670 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 920, 520, 670 using Euclid's Algorithm?

For arbitrary numbers 920, 520, 670 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 920, 520, 670 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 920, 520, 670?

HCF of 920, 520, 670 is 10 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 920, 520, 670 ? 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 920, 520, 670 using Euclid's algorithm i.e 10 quickly.

Detailed Method to Find the HCF of 920,520,670 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 920,520,670. This is how to do it.

Step 1: The first step is to use the division lemma with 920 and 520 because 920 is greater than 520

920 = 520 x 1 + 400

Step 2: Here, the reminder 520 is not 0, we must use division lemma to 400 and 520, to get

520 = 400 x 1 + 120

Step 3: We consider the new divisor 400 and the new remainder 120, and apply the division lemma to get

400 = 120 x 3 + 40

We consider the new divisor 120 and the new remainder 40, and apply the division lemma to get

120 = 40 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 40.Therefore, the HCF of 920 and 520 is equal to 40

Notice that 40 = HCF(120,40) = HCF(400,120) = HCF(520,400) = HCF(920,520) .

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 670 and 40 because 670 is greater than 40

670 = 40 x 16 + 30

Step 2: Here, the reminder 40 is not 0, we must use division lemma to 30 and 40, to get

40 = 30 x 1 + 10

Step 3: We consider the new divisor 30 and the new remainder 10, and apply the division lemma to get

30 = 10 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 10.Therefore, the HCF of 40 and 670 is equal to 10

Notice that 10 = HCF(30,10) = HCF(40,30) = HCF(670,40) .

Result

Hence, the HCF of 920, 520, 670 is equal to 10.

FAQ on HCF of 920, 520, 670 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 920, 520, 670?

Answer: The HCF of 920, 520, 670 is 10.