Highest Common Factor of 8571, 1971 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 8571, 1971 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8571, 1971 is 3 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 8571, 1971 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 8571, 1971 is 3.
HCF(8571, 1971) = 3
HCF of 8571, 1971 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8571, 1971 is 3.
Highest Common Factor of 8571,1971 is 3
Step 1: Since 8571 > 1971, we apply the division lemma to 8571 and 1971, to get
8571 = 1971 x 4 + 687
Step 2: Since the reminder 1971 ≠ 0, we apply division lemma to 687 and 1971, to get
1971 = 687 x 2 + 597
Step 3: We consider the new divisor 687 and the new remainder 597, and apply the division lemma to get
687 = 597 x 1 + 90
We consider the new divisor 597 and the new remainder 90,and apply the division lemma to get
597 = 90 x 6 + 57
We consider the new divisor 90 and the new remainder 57,and apply the division lemma to get
90 = 57 x 1 + 33
We consider the new divisor 57 and the new remainder 33,and apply the division lemma to get
57 = 33 x 1 + 24
We consider the new divisor 33 and the new remainder 24,and apply the division lemma to get
33 = 24 x 1 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8571 and 1971 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(33,24) = HCF(57,33) = HCF(90,57) = HCF(597,90) = HCF(687,597) = HCF(1971,687) = HCF(8571,1971) .
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Frequently Asked Questions on HCF of 8571, 1971 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 8571, 1971?
Answer: HCF of 8571, 1971 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8571, 1971 using Euclid's Algorithm?
Answer: For arbitrary numbers 8571, 1971 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.