Highest Common Factor of 412, 586 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 412, 586 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 412, 586 is 2 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 412, 586 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 412, 586 is 2.
HCF(412, 586) = 2
HCF of 412, 586 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 412, 586 is 2.
Highest Common Factor of 412,586 is 2
Step 1: Since 586 > 412, we apply the division lemma to 586 and 412, to get
586 = 412 x 1 + 174
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 174 and 412, to get
412 = 174 x 2 + 64
Step 3: We consider the new divisor 174 and the new remainder 64, and apply the division lemma to get
174 = 64 x 2 + 46
We consider the new divisor 64 and the new remainder 46,and apply the division lemma to get
64 = 46 x 1 + 18
We consider the new divisor 46 and the new remainder 18,and apply the division lemma to get
46 = 18 x 2 + 10
We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get
18 = 10 x 1 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 412 and 586 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(46,18) = HCF(64,46) = HCF(174,64) = HCF(412,174) = HCF(586,412) .
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Frequently Asked Questions on HCF of 412, 586 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 412, 586?
Answer: HCF of 412, 586 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 412, 586 using Euclid's Algorithm?
Answer: For arbitrary numbers 412, 586 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.