Highest Common Factor of 697, 6686, 4969 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 697, 6686, 4969 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 697, 6686, 4969 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 697, 6686, 4969 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 697, 6686, 4969 is 1.

HCF(697, 6686, 4969) = 1

HCF of 697, 6686, 4969 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 697, 6686, 4969 is 1.

Highest Common Factor of 697,6686,4969 using Euclid's algorithm

Highest Common Factor of 697,6686,4969 is 1

Step 1: Since 6686 > 697, we apply the division lemma to 6686 and 697, to get

6686 = 697 x 9 + 413

Step 2: Since the reminder 697 ≠ 0, we apply division lemma to 413 and 697, to get

697 = 413 x 1 + 284

Step 3: We consider the new divisor 413 and the new remainder 284, and apply the division lemma to get

413 = 284 x 1 + 129

We consider the new divisor 284 and the new remainder 129,and apply the division lemma to get

284 = 129 x 2 + 26

We consider the new divisor 129 and the new remainder 26,and apply the division lemma to get

129 = 26 x 4 + 25

We consider the new divisor 26 and the new remainder 25,and apply the division lemma to get

26 = 25 x 1 + 1

We consider the new divisor 25 and the new remainder 1,and apply the division lemma to get

25 = 1 x 25 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 697 and 6686 is 1

Notice that 1 = HCF(25,1) = HCF(26,25) = HCF(129,26) = HCF(284,129) = HCF(413,284) = HCF(697,413) = HCF(6686,697) .

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

Step 1: Since 4969 > 1, we apply the division lemma to 4969 and 1, to get

4969 = 1 x 4969 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 4969 is 1

Notice that 1 = HCF(4969,1) .

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Frequently Asked Questions on HCF of 697, 6686, 4969 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 697, 6686, 4969?

Answer: HCF of 697, 6686, 4969 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 697, 6686, 4969 using Euclid's Algorithm?

Answer: For arbitrary numbers 697, 6686, 4969 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.