Highest Common Factor of 403, 913, 20, 514 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 403, 913, 20, 514 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 403, 913, 20, 514 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 403, 913, 20, 514 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 403, 913, 20, 514 is 1.
HCF(403, 913, 20, 514) = 1
HCF of 403, 913, 20, 514 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 403, 913, 20, 514 is 1.
Highest Common Factor of 403,913,20,514 is 1
Step 1: Since 913 > 403, we apply the division lemma to 913 and 403, to get
913 = 403 x 2 + 107
Step 2: Since the reminder 403 ≠ 0, we apply division lemma to 107 and 403, to get
403 = 107 x 3 + 82
Step 3: We consider the new divisor 107 and the new remainder 82, and apply the division lemma to get
107 = 82 x 1 + 25
We consider the new divisor 82 and the new remainder 25,and apply the division lemma to get
82 = 25 x 3 + 7
We consider the new divisor 25 and the new remainder 7,and apply the division lemma to get
25 = 7 x 3 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 403 and 913 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(25,7) = HCF(82,25) = HCF(107,82) = HCF(403,107) = HCF(913,403) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 20 > 1, we apply the division lemma to 20 and 1, to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 20 is 1
Notice that 1 = HCF(20,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 514 > 1, we apply the division lemma to 514 and 1, to get
514 = 1 x 514 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 514 is 1
Notice that 1 = HCF(514,1) .
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Frequently Asked Questions on HCF of 403, 913, 20, 514 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 403, 913, 20, 514?
Answer: HCF of 403, 913, 20, 514 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 403, 913, 20, 514 using Euclid's Algorithm?
Answer: For arbitrary numbers 403, 913, 20, 514 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.