Highest Common Factor of 686, 396, 853 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 686, 396, 853 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 686, 396, 853 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 686, 396, 853 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 686, 396, 853 is 1.

HCF(686, 396, 853) = 1

HCF of 686, 396, 853 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 686, 396, 853 is 1.

Highest Common Factor of 686,396,853 using Euclid's algorithm

Highest Common Factor of 686,396,853 is 1

Step 1: Since 686 > 396, we apply the division lemma to 686 and 396, to get

686 = 396 x 1 + 290

Step 2: Since the reminder 396 ≠ 0, we apply division lemma to 290 and 396, to get

396 = 290 x 1 + 106

Step 3: We consider the new divisor 290 and the new remainder 106, and apply the division lemma to get

290 = 106 x 2 + 78

We consider the new divisor 106 and the new remainder 78,and apply the division lemma to get

106 = 78 x 1 + 28

We consider the new divisor 78 and the new remainder 28,and apply the division lemma to get

78 = 28 x 2 + 22

We consider the new divisor 28 and the new remainder 22,and apply the division lemma to get

28 = 22 x 1 + 6

We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get

22 = 6 x 3 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 686 and 396 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(28,22) = HCF(78,28) = HCF(106,78) = HCF(290,106) = HCF(396,290) = HCF(686,396) .

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

Step 1: Since 853 > 2, we apply the division lemma to 853 and 2, to get

853 = 2 x 426 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 853 is 1

Notice that 1 = HCF(2,1) = HCF(853,2) .

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Frequently Asked Questions on HCF of 686, 396, 853 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 686, 396, 853?

Answer: HCF of 686, 396, 853 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 686, 396, 853 using Euclid's Algorithm?

Answer: For arbitrary numbers 686, 396, 853 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.