Highest Common Factor of 7102, 6171 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 7102, 6171 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 7102, 6171 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 7102, 6171 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 7102, 6171 is 1.
HCF(7102, 6171) = 1
HCF of 7102, 6171 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7102, 6171 is 1.
Highest Common Factor of 7102,6171 is 1
Step 1: Since 7102 > 6171, we apply the division lemma to 7102 and 6171, to get
7102 = 6171 x 1 + 931
Step 2: Since the reminder 6171 ≠ 0, we apply division lemma to 931 and 6171, to get
6171 = 931 x 6 + 585
Step 3: We consider the new divisor 931 and the new remainder 585, and apply the division lemma to get
931 = 585 x 1 + 346
We consider the new divisor 585 and the new remainder 346,and apply the division lemma to get
585 = 346 x 1 + 239
We consider the new divisor 346 and the new remainder 239,and apply the division lemma to get
346 = 239 x 1 + 107
We consider the new divisor 239 and the new remainder 107,and apply the division lemma to get
239 = 107 x 2 + 25
We consider the new divisor 107 and the new remainder 25,and apply the division lemma to get
107 = 25 x 4 + 7
We consider the new divisor 25 and the new remainder 7,and apply the division lemma to get
25 = 7 x 3 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 7102 and 6171 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(25,7) = HCF(107,25) = HCF(239,107) = HCF(346,239) = HCF(585,346) = HCF(931,585) = HCF(6171,931) = HCF(7102,6171) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 7102, 6171 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 7102, 6171?
Answer: HCF of 7102, 6171 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7102, 6171 using Euclid's Algorithm?
Answer: For arbitrary numbers 7102, 6171 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.