Highest Common Factor of 516, 317, 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 516, 317, 364 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 516, 317, 364 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 516, 317, 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 516, 317, 364 is 1.
HCF(516, 317, 364) = 1
HCF of 516, 317, 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 516, 317, 364 is 1.
Highest Common Factor of 516,317,364 is 1
Step 1: Since 516 > 317, we apply the division lemma to 516 and 317, to get
516 = 317 x 1 + 199
Step 2: Since the reminder 317 ≠ 0, we apply division lemma to 199 and 317, to get
317 = 199 x 1 + 118
Step 3: We consider the new divisor 199 and the new remainder 118, and apply the division lemma to get
199 = 118 x 1 + 81
We consider the new divisor 118 and the new remainder 81,and apply the division lemma to get
118 = 81 x 1 + 37
We consider the new divisor 81 and the new remainder 37,and apply the division lemma to get
81 = 37 x 2 + 7
We consider the new divisor 37 and the new remainder 7,and apply the division lemma to get
37 = 7 x 5 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 516 and 317 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(37,7) = HCF(81,37) = HCF(118,81) = HCF(199,118) = HCF(317,199) = HCF(516,317) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 364 > 1, we apply the division lemma to 364 and 1, to get
364 = 1 x 364 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 364 is 1
Notice that 1 = HCF(364,1) .
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Frequently Asked Questions on HCF of 516, 317, 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 516, 317, 364?
Answer: HCF of 516, 317, 364 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 516, 317, 364 using Euclid's Algorithm?
Answer: For arbitrary numbers 516, 317, 364 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.