Highest Common Factor of 826, 8726 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 826, 8726 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 826, 8726 is 2 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 826, 8726 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 826, 8726 is 2.
HCF(826, 8726) = 2
HCF of 826, 8726 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 826, 8726 is 2.
Highest Common Factor of 826,8726 is 2
Step 1: Since 8726 > 826, we apply the division lemma to 8726 and 826, to get
8726 = 826 x 10 + 466
Step 2: Since the reminder 826 ≠ 0, we apply division lemma to 466 and 826, to get
826 = 466 x 1 + 360
Step 3: We consider the new divisor 466 and the new remainder 360, and apply the division lemma to get
466 = 360 x 1 + 106
We consider the new divisor 360 and the new remainder 106,and apply the division lemma to get
360 = 106 x 3 + 42
We consider the new divisor 106 and the new remainder 42,and apply the division lemma to get
106 = 42 x 2 + 22
We consider the new divisor 42 and the new remainder 22,and apply the division lemma to get
42 = 22 x 1 + 20
We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 826 and 8726 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(42,22) = HCF(106,42) = HCF(360,106) = HCF(466,360) = HCF(826,466) = HCF(8726,826) .
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Frequently Asked Questions on HCF of 826, 8726 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 826, 8726?
Answer: HCF of 826, 8726 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 826, 8726 using Euclid's Algorithm?
Answer: For arbitrary numbers 826, 8726 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.