Highest Common Factor of 691, 301, 617 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 691, 301, 617 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 691, 301, 617 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 691, 301, 617 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 691, 301, 617 is 1.

HCF(691, 301, 617) = 1

HCF of 691, 301, 617 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 691, 301, 617 is 1.

Highest Common Factor of 691,301,617 using Euclid's algorithm

Highest Common Factor of 691,301,617 is 1

Step 1: Since 691 > 301, we apply the division lemma to 691 and 301, to get

691 = 301 x 2 + 89

Step 2: Since the reminder 301 ≠ 0, we apply division lemma to 89 and 301, to get

301 = 89 x 3 + 34

Step 3: We consider the new divisor 89 and the new remainder 34, and apply the division lemma to get

89 = 34 x 2 + 21

We consider the new divisor 34 and the new remainder 21,and apply the division lemma to get

34 = 21 x 1 + 13

We consider the new divisor 21 and the new remainder 13,and apply the division lemma to get

21 = 13 x 1 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 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 691 and 301 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(21,13) = HCF(34,21) = HCF(89,34) = HCF(301,89) = HCF(691,301) .

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

Step 1: Since 617 > 1, we apply the division lemma to 617 and 1, to get

617 = 1 x 617 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 617 is 1

Notice that 1 = HCF(617,1) .

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Frequently Asked Questions on HCF of 691, 301, 617 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 691, 301, 617?

Answer: HCF of 691, 301, 617 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 691, 301, 617 using Euclid's Algorithm?

Answer: For arbitrary numbers 691, 301, 617 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.