Highest Common Factor of 8114, 1424 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 8114, 1424 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8114, 1424 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 8114, 1424 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 8114, 1424 is 2.
HCF(8114, 1424) = 2
HCF of 8114, 1424 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8114, 1424 is 2.
Highest Common Factor of 8114,1424 is 2
Step 1: Since 8114 > 1424, we apply the division lemma to 8114 and 1424, to get
8114 = 1424 x 5 + 994
Step 2: Since the reminder 1424 ≠ 0, we apply division lemma to 994 and 1424, to get
1424 = 994 x 1 + 430
Step 3: We consider the new divisor 994 and the new remainder 430, and apply the division lemma to get
994 = 430 x 2 + 134
We consider the new divisor 430 and the new remainder 134,and apply the division lemma to get
430 = 134 x 3 + 28
We consider the new divisor 134 and the new remainder 28,and apply the division lemma to get
134 = 28 x 4 + 22
We consider the new divisor 28 and the new remainder 22,and apply the division lemma to get
28 = 22 x 1 + 6
We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8114 and 1424 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(28,22) = HCF(134,28) = HCF(430,134) = HCF(994,430) = HCF(1424,994) = HCF(8114,1424) .
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Frequently Asked Questions on HCF of 8114, 1424 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 8114, 1424?
Answer: HCF of 8114, 1424 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8114, 1424 using Euclid's Algorithm?
Answer: For arbitrary numbers 8114, 1424 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
