Highest Common Factor of 2191, 2670 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 2191, 2670 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2191, 2670 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 2191, 2670 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 2191, 2670 is 1.
HCF(2191, 2670) = 1
HCF of 2191, 2670 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2191, 2670 is 1.
Highest Common Factor of 2191,2670 is 1
Step 1: Since 2670 > 2191, we apply the division lemma to 2670 and 2191, to get
2670 = 2191 x 1 + 479
Step 2: Since the reminder 2191 ≠ 0, we apply division lemma to 479 and 2191, to get
2191 = 479 x 4 + 275
Step 3: We consider the new divisor 479 and the new remainder 275, and apply the division lemma to get
479 = 275 x 1 + 204
We consider the new divisor 275 and the new remainder 204,and apply the division lemma to get
275 = 204 x 1 + 71
We consider the new divisor 204 and the new remainder 71,and apply the division lemma to get
204 = 71 x 2 + 62
We consider the new divisor 71 and the new remainder 62,and apply the division lemma to get
71 = 62 x 1 + 9
We consider the new divisor 62 and the new remainder 9,and apply the division lemma to get
62 = 9 x 6 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2191 and 2670 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(62,9) = HCF(71,62) = HCF(204,71) = HCF(275,204) = HCF(479,275) = HCF(2191,479) = HCF(2670,2191) .
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Frequently Asked Questions on HCF of 2191, 2670 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 2191, 2670?
Answer: HCF of 2191, 2670 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2191, 2670 using Euclid's Algorithm?
Answer: For arbitrary numbers 2191, 2670 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.