Highest Common Factor of 684, 586, 259 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 684, 586, 259 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 684, 586, 259 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 684, 586, 259 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 684, 586, 259 is 1.
HCF(684, 586, 259) = 1
HCF of 684, 586, 259 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 684, 586, 259 is 1.
Highest Common Factor of 684,586,259 is 1
Step 1: Since 684 > 586, we apply the division lemma to 684 and 586, to get
684 = 586 x 1 + 98
Step 2: Since the reminder 586 ≠ 0, we apply division lemma to 98 and 586, to get
586 = 98 x 5 + 96
Step 3: We consider the new divisor 98 and the new remainder 96, and apply the division lemma to get
98 = 96 x 1 + 2
We consider the new divisor 96 and the new remainder 2, and apply the division lemma to get
96 = 2 x 48 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 684 and 586 is 2
Notice that 2 = HCF(96,2) = HCF(98,96) = HCF(586,98) = HCF(684,586) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 259 > 2, we apply the division lemma to 259 and 2, to get
259 = 2 x 129 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 259 is 1
Notice that 1 = HCF(2,1) = HCF(259,2) .
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Frequently Asked Questions on HCF of 684, 586, 259 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 684, 586, 259?
Answer: HCF of 684, 586, 259 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 684, 586, 259 using Euclid's Algorithm?
Answer: For arbitrary numbers 684, 586, 259 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.