Highest Common Factor of 905, 420, 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 905, 420, 586 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 905, 420, 586 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 905, 420, 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 905, 420, 586 is 1.
HCF(905, 420, 586) = 1
HCF of 905, 420, 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 905, 420, 586 is 1.
Highest Common Factor of 905,420,586 is 1
Step 1: Since 905 > 420, we apply the division lemma to 905 and 420, to get
905 = 420 x 2 + 65
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 65 and 420, to get
420 = 65 x 6 + 30
Step 3: We consider the new divisor 65 and the new remainder 30, and apply the division lemma to get
65 = 30 x 2 + 5
We consider the new divisor 30 and the new remainder 5, and apply the division lemma to get
30 = 5 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 905 and 420 is 5
Notice that 5 = HCF(30,5) = HCF(65,30) = HCF(420,65) = HCF(905,420) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 586 > 5, we apply the division lemma to 586 and 5, to get
586 = 5 x 117 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 586 is 1
Notice that 1 = HCF(5,1) = HCF(586,5) .
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Frequently Asked Questions on HCF of 905, 420, 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 905, 420, 586?
Answer: HCF of 905, 420, 586 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 905, 420, 586 using Euclid's Algorithm?
Answer: For arbitrary numbers 905, 420, 586 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.