Highest Common Factor of 398, 586, 643 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 398, 586, 643 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 398, 586, 643 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 398, 586, 643 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 398, 586, 643 is 1.
HCF(398, 586, 643) = 1
HCF of 398, 586, 643 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 398, 586, 643 is 1.
Highest Common Factor of 398,586,643 is 1
Step 1: Since 586 > 398, we apply the division lemma to 586 and 398, to get
586 = 398 x 1 + 188
Step 2: Since the reminder 398 ≠ 0, we apply division lemma to 188 and 398, to get
398 = 188 x 2 + 22
Step 3: We consider the new divisor 188 and the new remainder 22, and apply the division lemma to get
188 = 22 x 8 + 12
We consider the new divisor 22 and the new remainder 12,and apply the division lemma to get
22 = 12 x 1 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 398 and 586 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(22,12) = HCF(188,22) = HCF(398,188) = HCF(586,398) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 643 > 2, we apply the division lemma to 643 and 2, to get
643 = 2 x 321 + 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 643 is 1
Notice that 1 = HCF(2,1) = HCF(643,2) .
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Frequently Asked Questions on HCF of 398, 586, 643 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 398, 586, 643?
Answer: HCF of 398, 586, 643 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 398, 586, 643 using Euclid's Algorithm?
Answer: For arbitrary numbers 398, 586, 643 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.