How to find HCF of 70, 90, 80 using Euclid's Algorithm?

For arbitrary numbers 70, 90, 80 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 70, 90, 80 using Euclid's Algorithm?

For arbitrary numbers 70, 90, 80 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 70, 90, 80 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 70, 90, 80?

HCF of 70, 90, 80 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 70, 90, 80 ? 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 70, 90, 80 using Euclid's algorithm i.e 10 quickly.

Detailed Method to Find the HCF of 70,90,80 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 70,90,80. This is how to do it.

Step 1: The first step is to use the division lemma with 90 and 70 because 90 is greater than 70

90 = 70 x 1 + 20

Step 2: Here, the reminder 70 is not 0, we must use division lemma to 20 and 70, to get

70 = 20 x 3 + 10

Step 3: We consider the new divisor 20 and the new remainder 10, and apply the division lemma to get

20 = 10 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 10.Therefore, the HCF of 70 and 90 is equal to 10

Notice that 10 = HCF(20,10) = HCF(70,20) = HCF(90,70) .

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 80 and 10 because 80 is greater than 10

80 = 10 x 8 + 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 10 and 80 is equal to 10

Notice that 10 = HCF(80,10) .

Result

Hence, the HCF of 70, 90, 80 is equal to 10.

FAQ on HCF of 70, 90, 80 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 70, 90, 80?

Answer: The HCF of 70, 90, 80 is 10.