Highest Common Factor of 6117, 3171 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 6117, 3171 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 6117, 3171 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 6117, 3171 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 6117, 3171 is 3.
HCF(6117, 3171) = 3
HCF of 6117, 3171 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6117, 3171 is 3.
Highest Common Factor of 6117,3171 is 3
Step 1: Since 6117 > 3171, we apply the division lemma to 6117 and 3171, to get
6117 = 3171 x 1 + 2946
Step 2: Since the reminder 3171 ≠ 0, we apply division lemma to 2946 and 3171, to get
3171 = 2946 x 1 + 225
Step 3: We consider the new divisor 2946 and the new remainder 225, and apply the division lemma to get
2946 = 225 x 13 + 21
We consider the new divisor 225 and the new remainder 21,and apply the division lemma to get
225 = 21 x 10 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 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 6117 and 3171 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(225,21) = HCF(2946,225) = HCF(3171,2946) = HCF(6117,3171) .
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Frequently Asked Questions on HCF of 6117, 3171 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 6117, 3171?
Answer: HCF of 6117, 3171 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6117, 3171 using Euclid's Algorithm?
Answer: For arbitrary numbers 6117, 3171 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.