Highest Common Factor of 686, 258, 291 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 686, 258, 291 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 686, 258, 291 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 686, 258, 291 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 686, 258, 291 is 1.
HCF(686, 258, 291) = 1
HCF of 686, 258, 291 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 686, 258, 291 is 1.
Highest Common Factor of 686,258,291 is 1
Step 1: Since 686 > 258, we apply the division lemma to 686 and 258, to get
686 = 258 x 2 + 170
Step 2: Since the reminder 258 ≠ 0, we apply division lemma to 170 and 258, to get
258 = 170 x 1 + 88
Step 3: We consider the new divisor 170 and the new remainder 88, and apply the division lemma to get
170 = 88 x 1 + 82
We consider the new divisor 88 and the new remainder 82,and apply the division lemma to get
88 = 82 x 1 + 6
We consider the new divisor 82 and the new remainder 6,and apply the division lemma to get
82 = 6 x 13 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 686 and 258 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(82,6) = HCF(88,82) = HCF(170,88) = HCF(258,170) = HCF(686,258) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 291 > 2, we apply the division lemma to 291 and 2, to get
291 = 2 x 145 + 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 291 is 1
Notice that 1 = HCF(2,1) = HCF(291,2) .
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Frequently Asked Questions on HCF of 686, 258, 291 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 686, 258, 291?
Answer: HCF of 686, 258, 291 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 686, 258, 291 using Euclid's Algorithm?
Answer: For arbitrary numbers 686, 258, 291 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.