Highest Common Factor of 687, 828, 209 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 687, 828, 209 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 687, 828, 209 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 687, 828, 209 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 687, 828, 209 is 1.

HCF(687, 828, 209) = 1

HCF of 687, 828, 209 using Euclid's algorithm

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

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Highest common factor (HCF) of 687, 828, 209 is 1.

Highest Common Factor of 687,828,209 using Euclid's algorithm

Highest Common Factor of 687,828,209 is 1

Step 1: Since 828 > 687, we apply the division lemma to 828 and 687, to get

828 = 687 x 1 + 141

Step 2: Since the reminder 687 ≠ 0, we apply division lemma to 141 and 687, to get

687 = 141 x 4 + 123

Step 3: We consider the new divisor 141 and the new remainder 123, and apply the division lemma to get

141 = 123 x 1 + 18

We consider the new divisor 123 and the new remainder 18,and apply the division lemma to get

123 = 18 x 6 + 15

We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get

18 = 15 x 1 + 3

We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get

15 = 3 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 687 and 828 is 3

Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(123,18) = HCF(141,123) = HCF(687,141) = HCF(828,687) .

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

Step 1: Since 209 > 3, we apply the division lemma to 209 and 3, to get

209 = 3 x 69 + 2

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

3 = 2 x 1 + 1

Step 3: 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 3 and 209 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(209,3) .

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Frequently Asked Questions on HCF of 687, 828, 209 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 687, 828, 209?

Answer: HCF of 687, 828, 209 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 687, 828, 209 using Euclid's Algorithm?

Answer: For arbitrary numbers 687, 828, 209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.