Highest Common Factor of 516, 817, 763 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, 817, 763 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 516, 817, 763 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, 817, 763 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, 817, 763 is 1.
HCF(516, 817, 763) = 1
HCF of 516, 817, 763 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, 817, 763 is 1.
Highest Common Factor of 516,817,763 is 1
Step 1: Since 817 > 516, we apply the division lemma to 817 and 516, to get
817 = 516 x 1 + 301
Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 301 and 516, to get
516 = 301 x 1 + 215
Step 3: We consider the new divisor 301 and the new remainder 215, and apply the division lemma to get
301 = 215 x 1 + 86
We consider the new divisor 215 and the new remainder 86,and apply the division lemma to get
215 = 86 x 2 + 43
We consider the new divisor 86 and the new remainder 43,and apply the division lemma to get
86 = 43 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 43, the HCF of 516 and 817 is 43
Notice that 43 = HCF(86,43) = HCF(215,86) = HCF(301,215) = HCF(516,301) = HCF(817,516) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 763 > 43, we apply the division lemma to 763 and 43, to get
763 = 43 x 17 + 32
Step 2: Since the reminder 43 ≠ 0, we apply division lemma to 32 and 43, to get
43 = 32 x 1 + 11
Step 3: We consider the new divisor 32 and the new remainder 11, and apply the division lemma to get
32 = 11 x 2 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 43 and 763 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(32,11) = HCF(43,32) = HCF(763,43) .
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Frequently Asked Questions on HCF of 516, 817, 763 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, 817, 763?
Answer: HCF of 516, 817, 763 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 516, 817, 763 using Euclid's Algorithm?
Answer: For arbitrary numbers 516, 817, 763 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.