Highest Common Factor of 4214, 4066, 82894 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 4214, 4066, 82894 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 4214, 4066, 82894 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 4214, 4066, 82894 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 4214, 4066, 82894 is 2.
HCF(4214, 4066, 82894) = 2
HCF of 4214, 4066, 82894 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4214, 4066, 82894 is 2.
Highest Common Factor of 4214,4066,82894 is 2
Step 1: Since 4214 > 4066, we apply the division lemma to 4214 and 4066, to get
4214 = 4066 x 1 + 148
Step 2: Since the reminder 4066 ≠ 0, we apply division lemma to 148 and 4066, to get
4066 = 148 x 27 + 70
Step 3: We consider the new divisor 148 and the new remainder 70, and apply the division lemma to get
148 = 70 x 2 + 8
We consider the new divisor 70 and the new remainder 8,and apply the division lemma to get
70 = 8 x 8 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4214 and 4066 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(70,8) = HCF(148,70) = HCF(4066,148) = HCF(4214,4066) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 82894 > 2, we apply the division lemma to 82894 and 2, to get
82894 = 2 x 41447 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 82894 is 2
Notice that 2 = HCF(82894,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 4214, 4066, 82894 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 4214, 4066, 82894?
Answer: HCF of 4214, 4066, 82894 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4214, 4066, 82894 using Euclid's Algorithm?
Answer: For arbitrary numbers 4214, 4066, 82894 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.