Highest Common Factor of 814, 9404, 2614 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 814, 9404, 2614 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 814, 9404, 2614 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 814, 9404, 2614 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 814, 9404, 2614 is 2.
HCF(814, 9404, 2614) = 2
HCF of 814, 9404, 2614 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 814, 9404, 2614 is 2.
Highest Common Factor of 814,9404,2614 is 2
Step 1: Since 9404 > 814, we apply the division lemma to 9404 and 814, to get
9404 = 814 x 11 + 450
Step 2: Since the reminder 814 ≠ 0, we apply division lemma to 450 and 814, to get
814 = 450 x 1 + 364
Step 3: We consider the new divisor 450 and the new remainder 364, and apply the division lemma to get
450 = 364 x 1 + 86
We consider the new divisor 364 and the new remainder 86,and apply the division lemma to get
364 = 86 x 4 + 20
We consider the new divisor 86 and the new remainder 20,and apply the division lemma to get
86 = 20 x 4 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 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 814 and 9404 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(86,20) = HCF(364,86) = HCF(450,364) = HCF(814,450) = HCF(9404,814) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2614 > 2, we apply the division lemma to 2614 and 2, to get
2614 = 2 x 1307 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 2614 is 2
Notice that 2 = HCF(2614,2) .
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Frequently Asked Questions on HCF of 814, 9404, 2614 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 814, 9404, 2614?
Answer: HCF of 814, 9404, 2614 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 814, 9404, 2614 using Euclid's Algorithm?
Answer: For arbitrary numbers 814, 9404, 2614 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.