Highest Common Factor of 871, 8030 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, 8030 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 871, 8030 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, 8030 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, 8030 is 1.
HCF(871, 8030) = 1
HCF of 871, 8030 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 871, 8030 is 1.
Highest Common Factor of 871,8030 is 1
Step 1: Since 8030 > 871, we apply the division lemma to 8030 and 871, to get
8030 = 871 x 9 + 191
Step 2: Since the reminder 871 ≠ 0, we apply division lemma to 191 and 871, to get
871 = 191 x 4 + 107
Step 3: We consider the new divisor 191 and the new remainder 107, and apply the division lemma to get
191 = 107 x 1 + 84
We consider the new divisor 107 and the new remainder 84,and apply the division lemma to get
107 = 84 x 1 + 23
We consider the new divisor 84 and the new remainder 23,and apply the division lemma to get
84 = 23 x 3 + 15
We consider the new divisor 23 and the new remainder 15,and apply the division lemma to get
23 = 15 x 1 + 8
We consider the new divisor 15 and the new remainder 8,and apply the division lemma to get
15 = 8 x 1 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 871 and 8030 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(15,8) = HCF(23,15) = HCF(84,23) = HCF(107,84) = HCF(191,107) = HCF(871,191) = HCF(8030,871) .
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Frequently Asked Questions on HCF of 871, 8030 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, 8030?
Answer: HCF of 871, 8030 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 871, 8030 using Euclid's Algorithm?
Answer: For arbitrary numbers 871, 8030 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.