Highest Common Factor of 866, 4102 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 866, 4102 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 866, 4102 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 866, 4102 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 866, 4102 is 2.
HCF(866, 4102) = 2
HCF of 866, 4102 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 866, 4102 is 2.
Highest Common Factor of 866,4102 is 2
Step 1: Since 4102 > 866, we apply the division lemma to 4102 and 866, to get
4102 = 866 x 4 + 638
Step 2: Since the reminder 866 ≠ 0, we apply division lemma to 638 and 866, to get
866 = 638 x 1 + 228
Step 3: We consider the new divisor 638 and the new remainder 228, and apply the division lemma to get
638 = 228 x 2 + 182
We consider the new divisor 228 and the new remainder 182,and apply the division lemma to get
228 = 182 x 1 + 46
We consider the new divisor 182 and the new remainder 46,and apply the division lemma to get
182 = 46 x 3 + 44
We consider the new divisor 46 and the new remainder 44,and apply the division lemma to get
46 = 44 x 1 + 2
We consider the new divisor 44 and the new remainder 2,and apply the division lemma to get
44 = 2 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 866 and 4102 is 2
Notice that 2 = HCF(44,2) = HCF(46,44) = HCF(182,46) = HCF(228,182) = HCF(638,228) = HCF(866,638) = HCF(4102,866) .
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Frequently Asked Questions on HCF of 866, 4102 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 866, 4102?
Answer: HCF of 866, 4102 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 866, 4102 using Euclid's Algorithm?
Answer: For arbitrary numbers 866, 4102 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.