Highest Common Factor of 812, 514, 127 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 812, 514, 127 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 812, 514, 127 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 812, 514, 127 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 812, 514, 127 is 1.
HCF(812, 514, 127) = 1
HCF of 812, 514, 127 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 812, 514, 127 is 1.
Highest Common Factor of 812,514,127 is 1
Step 1: Since 812 > 514, we apply the division lemma to 812 and 514, to get
812 = 514 x 1 + 298
Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 298 and 514, to get
514 = 298 x 1 + 216
Step 3: We consider the new divisor 298 and the new remainder 216, and apply the division lemma to get
298 = 216 x 1 + 82
We consider the new divisor 216 and the new remainder 82,and apply the division lemma to get
216 = 82 x 2 + 52
We consider the new divisor 82 and the new remainder 52,and apply the division lemma to get
82 = 52 x 1 + 30
We consider the new divisor 52 and the new remainder 30,and apply the division lemma to get
52 = 30 x 1 + 22
We consider the new divisor 30 and the new remainder 22,and apply the division lemma to get
30 = 22 x 1 + 8
We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get
22 = 8 x 2 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 812 and 514 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(30,22) = HCF(52,30) = HCF(82,52) = HCF(216,82) = HCF(298,216) = HCF(514,298) = HCF(812,514) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 127 > 2, we apply the division lemma to 127 and 2, to get
127 = 2 x 63 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 127 is 1
Notice that 1 = HCF(2,1) = HCF(127,2) .
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Frequently Asked Questions on HCF of 812, 514, 127 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 812, 514, 127?
Answer: HCF of 812, 514, 127 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 812, 514, 127 using Euclid's Algorithm?
Answer: For arbitrary numbers 812, 514, 127 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
