Highest Common Factor of 516, 8514, 8413 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, 8514, 8413 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 516, 8514, 8413 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, 8514, 8413 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, 8514, 8413 is 1.
HCF(516, 8514, 8413) = 1
HCF of 516, 8514, 8413 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, 8514, 8413 is 1.
Highest Common Factor of 516,8514,8413 is 1
Step 1: Since 8514 > 516, we apply the division lemma to 8514 and 516, to get
8514 = 516 x 16 + 258
Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 258 and 516, to get
516 = 258 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 258, the HCF of 516 and 8514 is 258
Notice that 258 = HCF(516,258) = HCF(8514,516) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8413 > 258, we apply the division lemma to 8413 and 258, to get
8413 = 258 x 32 + 157
Step 2: Since the reminder 258 ≠ 0, we apply division lemma to 157 and 258, to get
258 = 157 x 1 + 101
Step 3: We consider the new divisor 157 and the new remainder 101, and apply the division lemma to get
157 = 101 x 1 + 56
We consider the new divisor 101 and the new remainder 56,and apply the division lemma to get
101 = 56 x 1 + 45
We consider the new divisor 56 and the new remainder 45,and apply the division lemma to get
56 = 45 x 1 + 11
We consider the new divisor 45 and the new remainder 11,and apply the division lemma to get
45 = 11 x 4 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 258 and 8413 is 1
Notice that 1 = HCF(11,1) = HCF(45,11) = HCF(56,45) = HCF(101,56) = HCF(157,101) = HCF(258,157) = HCF(8413,258) .
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Frequently Asked Questions on HCF of 516, 8514, 8413 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, 8514, 8413?
Answer: HCF of 516, 8514, 8413 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 516, 8514, 8413 using Euclid's Algorithm?
Answer: For arbitrary numbers 516, 8514, 8413 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.