Highest Common Factor of 314, 6701, 2091 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 314, 6701, 2091 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 314, 6701, 2091 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 314, 6701, 2091 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 314, 6701, 2091 is 1.
HCF(314, 6701, 2091) = 1
HCF of 314, 6701, 2091 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 314, 6701, 2091 is 1.
Highest Common Factor of 314,6701,2091 is 1
Step 1: Since 6701 > 314, we apply the division lemma to 6701 and 314, to get
6701 = 314 x 21 + 107
Step 2: Since the reminder 314 ≠ 0, we apply division lemma to 107 and 314, to get
314 = 107 x 2 + 100
Step 3: We consider the new divisor 107 and the new remainder 100, and apply the division lemma to get
107 = 100 x 1 + 7
We consider the new divisor 100 and the new remainder 7,and apply the division lemma to get
100 = 7 x 14 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 314 and 6701 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(100,7) = HCF(107,100) = HCF(314,107) = HCF(6701,314) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2091 > 1, we apply the division lemma to 2091 and 1, to get
2091 = 1 x 2091 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2091 is 1
Notice that 1 = HCF(2091,1) .
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Frequently Asked Questions on HCF of 314, 6701, 2091 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 314, 6701, 2091?
Answer: HCF of 314, 6701, 2091 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 314, 6701, 2091 using Euclid's Algorithm?
Answer: For arbitrary numbers 314, 6701, 2091 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.