Highest Common Factor of 871, 1342 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 871, 1342 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 871, 1342 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 871, 1342 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 871, 1342 is 1.

HCF(871, 1342) = 1

HCF of 871, 1342 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 871, 1342 is 1.

Highest Common Factor of 871,1342 using Euclid's algorithm

Highest Common Factor of 871,1342 is 1

Step 1: Since 1342 > 871, we apply the division lemma to 1342 and 871, to get

1342 = 871 x 1 + 471

Step 2: Since the reminder 871 ≠ 0, we apply division lemma to 471 and 871, to get

871 = 471 x 1 + 400

Step 3: We consider the new divisor 471 and the new remainder 400, and apply the division lemma to get

471 = 400 x 1 + 71

We consider the new divisor 400 and the new remainder 71,and apply the division lemma to get

400 = 71 x 5 + 45

We consider the new divisor 71 and the new remainder 45,and apply the division lemma to get

71 = 45 x 1 + 26

We consider the new divisor 45 and the new remainder 26,and apply the division lemma to get

45 = 26 x 1 + 19

We consider the new divisor 26 and the new remainder 19,and apply the division lemma to get

26 = 19 x 1 + 7

We consider the new divisor 19 and the new remainder 7,and apply the division lemma to get

19 = 7 x 2 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 871 and 1342 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(19,7) = HCF(26,19) = HCF(45,26) = HCF(71,45) = HCF(400,71) = HCF(471,400) = HCF(871,471) = HCF(1342,871) .

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Frequently Asked Questions on HCF of 871, 1342 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 871, 1342?

Answer: HCF of 871, 1342 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 871, 1342 using Euclid's Algorithm?

Answer: For arbitrary numbers 871, 1342 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.