Highest Common Factor of 514, 2373 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, 2373 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 514, 2373 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, 2373 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, 2373 is 1.
HCF(514, 2373) = 1
HCF of 514, 2373 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, 2373 is 1.
Highest Common Factor of 514,2373 is 1
Step 1: Since 2373 > 514, we apply the division lemma to 2373 and 514, to get
2373 = 514 x 4 + 317
Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 317 and 514, to get
514 = 317 x 1 + 197
Step 3: We consider the new divisor 317 and the new remainder 197, and apply the division lemma to get
317 = 197 x 1 + 120
We consider the new divisor 197 and the new remainder 120,and apply the division lemma to get
197 = 120 x 1 + 77
We consider the new divisor 120 and the new remainder 77,and apply the division lemma to get
120 = 77 x 1 + 43
We consider the new divisor 77 and the new remainder 43,and apply the division lemma to get
77 = 43 x 1 + 34
We consider the new divisor 43 and the new remainder 34,and apply the division lemma to get
43 = 34 x 1 + 9
We consider the new divisor 34 and the new remainder 9,and apply the division lemma to get
34 = 9 x 3 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 2373 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(34,9) = HCF(43,34) = HCF(77,43) = HCF(120,77) = HCF(197,120) = HCF(317,197) = HCF(514,317) = HCF(2373,514) .
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Frequently Asked Questions on HCF of 514, 2373 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, 2373?
Answer: HCF of 514, 2373 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 514, 2373 using Euclid's Algorithm?
Answer: For arbitrary numbers 514, 2373 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.