Highest Common Factor of 871, 260, 829 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, 260, 829 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 871, 260, 829 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, 260, 829 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, 260, 829 is 1.

HCF(871, 260, 829) = 1

HCF of 871, 260, 829 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, 260, 829 is 1.

Highest Common Factor of 871,260,829 using Euclid's algorithm

Highest Common Factor of 871,260,829 is 1

Step 1: Since 871 > 260, we apply the division lemma to 871 and 260, to get

871 = 260 x 3 + 91

Step 2: Since the reminder 260 ≠ 0, we apply division lemma to 91 and 260, to get

260 = 91 x 2 + 78

Step 3: We consider the new divisor 91 and the new remainder 78, and apply the division lemma to get

91 = 78 x 1 + 13

We consider the new divisor 78 and the new remainder 13, and apply the division lemma to get

78 = 13 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 871 and 260 is 13

Notice that 13 = HCF(78,13) = HCF(91,78) = HCF(260,91) = HCF(871,260) .

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

Step 1: Since 829 > 13, we apply the division lemma to 829 and 13, to get

829 = 13 x 63 + 10

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 10 and 13, to get

13 = 10 x 1 + 3

Step 3: We consider the new divisor 10 and the new remainder 3, and apply the division lemma to get

10 = 3 x 3 + 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 13 and 829 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(829,13) .

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Frequently Asked Questions on HCF of 871, 260, 829 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, 260, 829?

Answer: HCF of 871, 260, 829 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 871, 260, 829 using Euclid's Algorithm?

Answer: For arbitrary numbers 871, 260, 829 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.