Highest Common Factor of 585, 6784 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 585, 6784 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 585, 6784 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 585, 6784 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 585, 6784 is 1.
HCF(585, 6784) = 1
HCF of 585, 6784 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 585, 6784 is 1.
Highest Common Factor of 585,6784 is 1
Step 1: Since 6784 > 585, we apply the division lemma to 6784 and 585, to get
6784 = 585 x 11 + 349
Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 349 and 585, to get
585 = 349 x 1 + 236
Step 3: We consider the new divisor 349 and the new remainder 236, and apply the division lemma to get
349 = 236 x 1 + 113
We consider the new divisor 236 and the new remainder 113,and apply the division lemma to get
236 = 113 x 2 + 10
We consider the new divisor 113 and the new remainder 10,and apply the division lemma to get
113 = 10 x 11 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 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 585 and 6784 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(113,10) = HCF(236,113) = HCF(349,236) = HCF(585,349) = HCF(6784,585) .
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Frequently Asked Questions on HCF of 585, 6784 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 585, 6784?
Answer: HCF of 585, 6784 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 585, 6784 using Euclid's Algorithm?
Answer: For arbitrary numbers 585, 6784 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.