Highest Common Factor of 2137, 613 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 2137, 613 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2137, 613 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 2137, 613 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 2137, 613 is 1.
HCF(2137, 613) = 1
HCF of 2137, 613 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2137, 613 is 1.
Highest Common Factor of 2137,613 is 1
Step 1: Since 2137 > 613, we apply the division lemma to 2137 and 613, to get
2137 = 613 x 3 + 298
Step 2: Since the reminder 613 ≠ 0, we apply division lemma to 298 and 613, to get
613 = 298 x 2 + 17
Step 3: We consider the new divisor 298 and the new remainder 17, and apply the division lemma to get
298 = 17 x 17 + 9
We consider the new divisor 17 and the new remainder 9,and apply the division lemma to get
17 = 9 x 1 + 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 2137 and 613 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(17,9) = HCF(298,17) = HCF(613,298) = HCF(2137,613) .
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Frequently Asked Questions on HCF of 2137, 613 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 2137, 613?
Answer: HCF of 2137, 613 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2137, 613 using Euclid's Algorithm?
Answer: For arbitrary numbers 2137, 613 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.