Highest Common Factor of 871, 364, 99 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, 364, 99 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 871, 364, 99 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, 364, 99 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, 364, 99 is 1.

HCF(871, 364, 99) = 1

HCF of 871, 364, 99 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 871, 364, 99 is 1.

Highest Common Factor of 871,364,99 using Euclid's algorithm

Highest Common Factor of 871,364,99 is 1

Step 1: Since 871 > 364, we apply the division lemma to 871 and 364, to get

871 = 364 x 2 + 143

Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 143 and 364, to get

364 = 143 x 2 + 78

Step 3: We consider the new divisor 143 and the new remainder 78, and apply the division lemma to get

143 = 78 x 1 + 65

We consider the new divisor 78 and the new remainder 65,and apply the division lemma to get

78 = 65 x 1 + 13

We consider the new divisor 65 and the new remainder 13,and apply the division lemma to get

65 = 13 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 871 and 364 is 13

Notice that 13 = HCF(65,13) = HCF(78,65) = HCF(143,78) = HCF(364,143) = HCF(871,364) .

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

Step 1: Since 99 > 13, we apply the division lemma to 99 and 13, to get

99 = 13 x 7 + 8

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 8 and 13, to get

13 = 8 x 1 + 5

Step 3: 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 13 and 99 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(99,13) .

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Frequently Asked Questions on HCF of 871, 364, 99 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, 364, 99?

Answer: HCF of 871, 364, 99 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 871, 364, 99 using Euclid's Algorithm?

Answer: For arbitrary numbers 871, 364, 99 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.