Highest Common Factor of 514, 705 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, 705 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 514, 705 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 514, 705 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, 705 is 1.
HCF(514, 705) = 1
HCF of 514, 705 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, 705 is 1.
Highest Common Factor of 514,705 is 1
Step 1: Since 705 > 514, we apply the division lemma to 705 and 514, to get
705 = 514 x 1 + 191
Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 191 and 514, to get
514 = 191 x 2 + 132
Step 3: We consider the new divisor 191 and the new remainder 132, and apply the division lemma to get
191 = 132 x 1 + 59
We consider the new divisor 132 and the new remainder 59,and apply the division lemma to get
132 = 59 x 2 + 14
We consider the new divisor 59 and the new remainder 14,and apply the division lemma to get
59 = 14 x 4 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 514 and 705 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(59,14) = HCF(132,59) = HCF(191,132) = HCF(514,191) = HCF(705,514) .
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Frequently Asked Questions on HCF of 514, 705 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, 705?
Answer: HCF of 514, 705 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 514, 705 using Euclid's Algorithm?
Answer: For arbitrary numbers 514, 705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.