Highest Common Factor of 861, 971, 691 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 861, 971, 691 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 861, 971, 691 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 861, 971, 691 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 861, 971, 691 is 1.

HCF(861, 971, 691) = 1

HCF of 861, 971, 691 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 861, 971, 691 is 1.

Highest Common Factor of 861,971,691 using Euclid's algorithm

Highest Common Factor of 861,971,691 is 1

Step 1: Since 971 > 861, we apply the division lemma to 971 and 861, to get

971 = 861 x 1 + 110

Step 2: Since the reminder 861 ≠ 0, we apply division lemma to 110 and 861, to get

861 = 110 x 7 + 91

Step 3: We consider the new divisor 110 and the new remainder 91, and apply the division lemma to get

110 = 91 x 1 + 19

We consider the new divisor 91 and the new remainder 19,and apply the division lemma to get

91 = 19 x 4 + 15

We consider the new divisor 19 and the new remainder 15,and apply the division lemma to get

19 = 15 x 1 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

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 861 and 971 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(19,15) = HCF(91,19) = HCF(110,91) = HCF(861,110) = HCF(971,861) .

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

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

691 = 1 x 691 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 691 is 1

Notice that 1 = HCF(691,1) .

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Frequently Asked Questions on HCF of 861, 971, 691 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 861, 971, 691?

Answer: HCF of 861, 971, 691 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 861, 971, 691 using Euclid's Algorithm?

Answer: For arbitrary numbers 861, 971, 691 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.