Highest Common Factor of 691, 267, 471 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, 267, 471 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 691, 267, 471 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, 267, 471 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, 267, 471 is 1.

HCF(691, 267, 471) = 1

HCF of 691, 267, 471 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, 267, 471 is 1.

Highest Common Factor of 691,267,471 using Euclid's algorithm

Highest Common Factor of 691,267,471 is 1

Step 1: Since 691 > 267, we apply the division lemma to 691 and 267, to get

691 = 267 x 2 + 157

Step 2: Since the reminder 267 ≠ 0, we apply division lemma to 157 and 267, to get

267 = 157 x 1 + 110

Step 3: We consider the new divisor 157 and the new remainder 110, and apply the division lemma to get

157 = 110 x 1 + 47

We consider the new divisor 110 and the new remainder 47,and apply the division lemma to get

110 = 47 x 2 + 16

We consider the new divisor 47 and the new remainder 16,and apply the division lemma to get

47 = 16 x 2 + 15

We consider the new divisor 16 and the new remainder 15,and apply the division lemma to get

16 = 15 x 1 + 1

We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get

15 = 1 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 691 and 267 is 1

Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(47,16) = HCF(110,47) = HCF(157,110) = HCF(267,157) = HCF(691,267) .

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

Step 1: Since 471 > 1, we apply the division lemma to 471 and 1, to get

471 = 1 x 471 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 471 is 1

Notice that 1 = HCF(471,1) .

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Frequently Asked Questions on HCF of 691, 267, 471 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, 267, 471?

Answer: HCF of 691, 267, 471 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 691, 267, 471 using Euclid's Algorithm?

Answer: For arbitrary numbers 691, 267, 471 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.