Highest Common Factor of 7871, 4131 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 7871, 4131 i.e. 17 the largest integer that leaves a remainder zero for all numbers.
HCF of 7871, 4131 is 17 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 7871, 4131 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 7871, 4131 is 17.
HCF(7871, 4131) = 17
HCF of 7871, 4131 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7871, 4131 is 17.
Highest Common Factor of 7871,4131 is 17
Step 1: Since 7871 > 4131, we apply the division lemma to 7871 and 4131, to get
7871 = 4131 x 1 + 3740
Step 2: Since the reminder 4131 ≠ 0, we apply division lemma to 3740 and 4131, to get
4131 = 3740 x 1 + 391
Step 3: We consider the new divisor 3740 and the new remainder 391, and apply the division lemma to get
3740 = 391 x 9 + 221
We consider the new divisor 391 and the new remainder 221,and apply the division lemma to get
391 = 221 x 1 + 170
We consider the new divisor 221 and the new remainder 170,and apply the division lemma to get
221 = 170 x 1 + 51
We consider the new divisor 170 and the new remainder 51,and apply the division lemma to get
170 = 51 x 3 + 17
We consider the new divisor 51 and the new remainder 17,and apply the division lemma to get
51 = 17 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 7871 and 4131 is 17
Notice that 17 = HCF(51,17) = HCF(170,51) = HCF(221,170) = HCF(391,221) = HCF(3740,391) = HCF(4131,3740) = HCF(7871,4131) .
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Frequently Asked Questions on HCF of 7871, 4131 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 7871, 4131?
Answer: HCF of 7871, 4131 is 17 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7871, 4131 using Euclid's Algorithm?
Answer: For arbitrary numbers 7871, 4131 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
