Highest Common Factor of 514, 2710 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 514, 2710 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 514, 2710 is 2 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 514, 2710 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 514, 2710 is 2.
HCF(514, 2710) = 2
HCF of 514, 2710 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 514, 2710 is 2.
Highest Common Factor of 514,2710 is 2
Step 1: Since 2710 > 514, we apply the division lemma to 2710 and 514, to get
2710 = 514 x 5 + 140
Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 140 and 514, to get
514 = 140 x 3 + 94
Step 3: We consider the new divisor 140 and the new remainder 94, and apply the division lemma to get
140 = 94 x 1 + 46
We consider the new divisor 94 and the new remainder 46,and apply the division lemma to get
94 = 46 x 2 + 2
We consider the new divisor 46 and the new remainder 2,and apply the division lemma to get
46 = 2 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 514 and 2710 is 2
Notice that 2 = HCF(46,2) = HCF(94,46) = HCF(140,94) = HCF(514,140) = HCF(2710,514) .
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Frequently Asked Questions on HCF of 514, 2710 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 514, 2710?
Answer: HCF of 514, 2710 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 514, 2710 using Euclid's Algorithm?
Answer: For arbitrary numbers 514, 2710 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.