Highest Common Factor of 585, 364 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, 364 i.e. 13 the largest integer that leaves a remainder zero for all numbers.
HCF of 585, 364 is 13 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, 364 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, 364 is 13.
HCF(585, 364) = 13
HCF of 585, 364 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, 364 is 13.
Highest Common Factor of 585,364 is 13
Step 1: Since 585 > 364, we apply the division lemma to 585 and 364, to get
585 = 364 x 1 + 221
Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 221 and 364, to get
364 = 221 x 1 + 143
Step 3: We consider the new divisor 221 and the new remainder 143, and apply the division lemma to get
221 = 143 x 1 + 78
We consider the new divisor 143 and the new remainder 78,and apply the division lemma to get
143 = 78 x 1 + 65
We consider the new divisor 78 and the new remainder 65,and apply the division lemma to get
78 = 65 x 1 + 13
We consider the new divisor 65 and the new remainder 13,and apply the division lemma to get
65 = 13 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 585 and 364 is 13
Notice that 13 = HCF(65,13) = HCF(78,65) = HCF(143,78) = HCF(221,143) = HCF(364,221) = HCF(585,364) .
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Frequently Asked Questions on HCF of 585, 364 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, 364?
Answer: HCF of 585, 364 is 13 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 585, 364 using Euclid's Algorithm?
Answer: For arbitrary numbers 585, 364 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.