Highest Common Factor of 2438, 8214 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 2438, 8214 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2438, 8214 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 2438, 8214 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 2438, 8214 is 2.
HCF(2438, 8214) = 2
HCF of 2438, 8214 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2438, 8214 is 2.
Highest Common Factor of 2438,8214 is 2
Step 1: Since 8214 > 2438, we apply the division lemma to 8214 and 2438, to get
8214 = 2438 x 3 + 900
Step 2: Since the reminder 2438 ≠ 0, we apply division lemma to 900 and 2438, to get
2438 = 900 x 2 + 638
Step 3: We consider the new divisor 900 and the new remainder 638, and apply the division lemma to get
900 = 638 x 1 + 262
We consider the new divisor 638 and the new remainder 262,and apply the division lemma to get
638 = 262 x 2 + 114
We consider the new divisor 262 and the new remainder 114,and apply the division lemma to get
262 = 114 x 2 + 34
We consider the new divisor 114 and the new remainder 34,and apply the division lemma to get
114 = 34 x 3 + 12
We consider the new divisor 34 and the new remainder 12,and apply the division lemma to get
34 = 12 x 2 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2438 and 8214 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(34,12) = HCF(114,34) = HCF(262,114) = HCF(638,262) = HCF(900,638) = HCF(2438,900) = HCF(8214,2438) .
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Frequently Asked Questions on HCF of 2438, 8214 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 2438, 8214?
Answer: HCF of 2438, 8214 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2438, 8214 using Euclid's Algorithm?
Answer: For arbitrary numbers 2438, 8214 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.