Highest Common Factor of 365, 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 365, 586 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 365, 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 365, 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 365, 586 is 1.
HCF(365, 586) = 1
HCF of 365, 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 365, 586 is 1.
Highest Common Factor of 365,586 is 1
Step 1: Since 586 > 365, we apply the division lemma to 586 and 365, to get
586 = 365 x 1 + 221
Step 2: Since the reminder 365 ≠ 0, we apply division lemma to 221 and 365, to get
365 = 221 x 1 + 144
Step 3: We consider the new divisor 221 and the new remainder 144, and apply the division lemma to get
221 = 144 x 1 + 77
We consider the new divisor 144 and the new remainder 77,and apply the division lemma to get
144 = 77 x 1 + 67
We consider the new divisor 77 and the new remainder 67,and apply the division lemma to get
77 = 67 x 1 + 10
We consider the new divisor 67 and the new remainder 10,and apply the division lemma to get
67 = 10 x 6 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 365 and 586 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(67,10) = HCF(77,67) = HCF(144,77) = HCF(221,144) = HCF(365,221) = HCF(586,365) .
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Frequently Asked Questions on HCF of 365, 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 365, 586?
Answer: HCF of 365, 586 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 365, 586 using Euclid's Algorithm?
Answer: For arbitrary numbers 365, 586 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.