Highest Common Factor of 812, 9726, 2063 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 812, 9726, 2063 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 812, 9726, 2063 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 812, 9726, 2063 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 812, 9726, 2063 is 1.
HCF(812, 9726, 2063) = 1
HCF of 812, 9726, 2063 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 812, 9726, 2063 is 1.
Highest Common Factor of 812,9726,2063 is 1
Step 1: Since 9726 > 812, we apply the division lemma to 9726 and 812, to get
9726 = 812 x 11 + 794
Step 2: Since the reminder 812 ≠ 0, we apply division lemma to 794 and 812, to get
812 = 794 x 1 + 18
Step 3: We consider the new divisor 794 and the new remainder 18, and apply the division lemma to get
794 = 18 x 44 + 2
We consider the new divisor 18 and the new remainder 2, and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 812 and 9726 is 2
Notice that 2 = HCF(18,2) = HCF(794,18) = HCF(812,794) = HCF(9726,812) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2063 > 2, we apply the division lemma to 2063 and 2, to get
2063 = 2 x 1031 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 2063 is 1
Notice that 1 = HCF(2,1) = HCF(2063,2) .
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Frequently Asked Questions on HCF of 812, 9726, 2063 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 812, 9726, 2063?
Answer: HCF of 812, 9726, 2063 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 812, 9726, 2063 using Euclid's Algorithm?
Answer: For arbitrary numbers 812, 9726, 2063 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
