Highest Common Factor of 2134, 5689 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 2134, 5689 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2134, 5689 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 2134, 5689 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 2134, 5689 is 1.
HCF(2134, 5689) = 1
HCF of 2134, 5689 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2134, 5689 is 1.
Highest Common Factor of 2134,5689 is 1
Step 1: Since 5689 > 2134, we apply the division lemma to 5689 and 2134, to get
5689 = 2134 x 2 + 1421
Step 2: Since the reminder 2134 ≠ 0, we apply division lemma to 1421 and 2134, to get
2134 = 1421 x 1 + 713
Step 3: We consider the new divisor 1421 and the new remainder 713, and apply the division lemma to get
1421 = 713 x 1 + 708
We consider the new divisor 713 and the new remainder 708,and apply the division lemma to get
713 = 708 x 1 + 5
We consider the new divisor 708 and the new remainder 5,and apply the division lemma to get
708 = 5 x 141 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 2134 and 5689 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(708,5) = HCF(713,708) = HCF(1421,713) = HCF(2134,1421) = HCF(5689,2134) .
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Frequently Asked Questions on HCF of 2134, 5689 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 2134, 5689?
Answer: HCF of 2134, 5689 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2134, 5689 using Euclid's Algorithm?
Answer: For arbitrary numbers 2134, 5689 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.