Highest Common Factor of 108, 211, 686 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 108, 211, 686 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 108, 211, 686 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 108, 211, 686 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 108, 211, 686 is 1.

HCF(108, 211, 686) = 1

HCF of 108, 211, 686 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 108, 211, 686 is 1.

Highest Common Factor of 108,211,686 using Euclid's algorithm

Highest Common Factor of 108,211,686 is 1

Step 1: Since 211 > 108, we apply the division lemma to 211 and 108, to get

211 = 108 x 1 + 103

Step 2: Since the reminder 108 ≠ 0, we apply division lemma to 103 and 108, to get

108 = 103 x 1 + 5

Step 3: We consider the new divisor 103 and the new remainder 5, and apply the division lemma to get

103 = 5 x 20 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 108 and 211 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(103,5) = HCF(108,103) = HCF(211,108) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 686 > 1, we apply the division lemma to 686 and 1, to get

686 = 1 x 686 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 686 is 1

Notice that 1 = HCF(686,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 108, 211, 686 using Euclid's Algorithm

1. What is the Euclid division algorithm?

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

2. what is the HCF of 108, 211, 686?

Answer: HCF of 108, 211, 686 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 108, 211, 686 using Euclid's Algorithm?

Answer: For arbitrary numbers 108, 211, 686 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.