Highest Common Factor of 813, 31205 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 813, 31205 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 813, 31205 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 813, 31205 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 813, 31205 is 1.
HCF(813, 31205) = 1
HCF of 813, 31205 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 813, 31205 is 1.
Highest Common Factor of 813,31205 is 1
Step 1: Since 31205 > 813, we apply the division lemma to 31205 and 813, to get
31205 = 813 x 38 + 311
Step 2: Since the reminder 813 ≠ 0, we apply division lemma to 311 and 813, to get
813 = 311 x 2 + 191
Step 3: We consider the new divisor 311 and the new remainder 191, and apply the division lemma to get
311 = 191 x 1 + 120
We consider the new divisor 191 and the new remainder 120,and apply the division lemma to get
191 = 120 x 1 + 71
We consider the new divisor 120 and the new remainder 71,and apply the division lemma to get
120 = 71 x 1 + 49
We consider the new divisor 71 and the new remainder 49,and apply the division lemma to get
71 = 49 x 1 + 22
We consider the new divisor 49 and the new remainder 22,and apply the division lemma to get
49 = 22 x 2 + 5
We consider the new divisor 22 and the new remainder 5,and apply the division lemma to get
22 = 5 x 4 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 813 and 31205 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(22,5) = HCF(49,22) = HCF(71,49) = HCF(120,71) = HCF(191,120) = HCF(311,191) = HCF(813,311) = HCF(31205,813) .
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Frequently Asked Questions on HCF of 813, 31205 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 813, 31205?
Answer: HCF of 813, 31205 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 813, 31205 using Euclid's Algorithm?
Answer: For arbitrary numbers 813, 31205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.