Highest Common Factor of 638, 4214, 8290 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 638, 4214, 8290 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 638, 4214, 8290 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 638, 4214, 8290 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 638, 4214, 8290 is 2.
HCF(638, 4214, 8290) = 2
HCF of 638, 4214, 8290 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 638, 4214, 8290 is 2.
Highest Common Factor of 638,4214,8290 is 2
Step 1: Since 4214 > 638, we apply the division lemma to 4214 and 638, to get
4214 = 638 x 6 + 386
Step 2: Since the reminder 638 ≠ 0, we apply division lemma to 386 and 638, to get
638 = 386 x 1 + 252
Step 3: We consider the new divisor 386 and the new remainder 252, and apply the division lemma to get
386 = 252 x 1 + 134
We consider the new divisor 252 and the new remainder 134,and apply the division lemma to get
252 = 134 x 1 + 118
We consider the new divisor 134 and the new remainder 118,and apply the division lemma to get
134 = 118 x 1 + 16
We consider the new divisor 118 and the new remainder 16,and apply the division lemma to get
118 = 16 x 7 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 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 638 and 4214 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(118,16) = HCF(134,118) = HCF(252,134) = HCF(386,252) = HCF(638,386) = HCF(4214,638) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8290 > 2, we apply the division lemma to 8290 and 2, to get
8290 = 2 x 4145 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 8290 is 2
Notice that 2 = HCF(8290,2) .
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Frequently Asked Questions on HCF of 638, 4214, 8290 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 638, 4214, 8290?
Answer: HCF of 638, 4214, 8290 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 638, 4214, 8290 using Euclid's Algorithm?
Answer: For arbitrary numbers 638, 4214, 8290 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.