Highest Common Factor of 868, 676, 687 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 868, 676, 687 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 868, 676, 687 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 868, 676, 687 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 868, 676, 687 is 1.

HCF(868, 676, 687) = 1

HCF of 868, 676, 687 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 868, 676, 687 is 1.

Highest Common Factor of 868,676,687 using Euclid's algorithm

Highest Common Factor of 868,676,687 is 1

Step 1: Since 868 > 676, we apply the division lemma to 868 and 676, to get

868 = 676 x 1 + 192

Step 2: Since the reminder 676 ≠ 0, we apply division lemma to 192 and 676, to get

676 = 192 x 3 + 100

Step 3: We consider the new divisor 192 and the new remainder 100, and apply the division lemma to get

192 = 100 x 1 + 92

We consider the new divisor 100 and the new remainder 92,and apply the division lemma to get

100 = 92 x 1 + 8

We consider the new divisor 92 and the new remainder 8,and apply the division lemma to get

92 = 8 x 11 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 868 and 676 is 4

Notice that 4 = HCF(8,4) = HCF(92,8) = HCF(100,92) = HCF(192,100) = HCF(676,192) = HCF(868,676) .

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

Step 1: Since 687 > 4, we apply the division lemma to 687 and 4, to get

687 = 4 x 171 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 687 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(687,4) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 868, 676, 687 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 868, 676, 687?

Answer: HCF of 868, 676, 687 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 868, 676, 687 using Euclid's Algorithm?

Answer: For arbitrary numbers 868, 676, 687 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.