Highest Common Factor of 586, 798, 51 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 586, 798, 51 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 586, 798, 51 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 586, 798, 51 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 586, 798, 51 is 1.
HCF(586, 798, 51) = 1
HCF of 586, 798, 51 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 586, 798, 51 is 1.
Highest Common Factor of 586,798,51 is 1
Step 1: Since 798 > 586, we apply the division lemma to 798 and 586, to get
798 = 586 x 1 + 212
Step 2: Since the reminder 586 ≠ 0, we apply division lemma to 212 and 586, to get
586 = 212 x 2 + 162
Step 3: We consider the new divisor 212 and the new remainder 162, and apply the division lemma to get
212 = 162 x 1 + 50
We consider the new divisor 162 and the new remainder 50,and apply the division lemma to get
162 = 50 x 3 + 12
We consider the new divisor 50 and the new remainder 12,and apply the division lemma to get
50 = 12 x 4 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 586 and 798 is 2
Notice that 2 = HCF(12,2) = HCF(50,12) = HCF(162,50) = HCF(212,162) = HCF(586,212) = HCF(798,586) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 51 > 2, we apply the division lemma to 51 and 2, to get
51 = 2 x 25 + 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 51 is 1
Notice that 1 = HCF(2,1) = HCF(51,2) .
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Frequently Asked Questions on HCF of 586, 798, 51 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 586, 798, 51?
Answer: HCF of 586, 798, 51 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 586, 798, 51 using Euclid's Algorithm?
Answer: For arbitrary numbers 586, 798, 51 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.