Highest Common Factor of 681, 2238, 8284 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 681, 2238, 8284 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 681, 2238, 8284 is 1 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 681, 2238, 8284 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 681, 2238, 8284 is 1.
HCF(681, 2238, 8284) = 1
HCF of 681, 2238, 8284 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 681, 2238, 8284 is 1.
Highest Common Factor of 681,2238,8284 is 1
Step 1: Since 2238 > 681, we apply the division lemma to 2238 and 681, to get
2238 = 681 x 3 + 195
Step 2: Since the reminder 681 ≠ 0, we apply division lemma to 195 and 681, to get
681 = 195 x 3 + 96
Step 3: We consider the new divisor 195 and the new remainder 96, and apply the division lemma to get
195 = 96 x 2 + 3
We consider the new divisor 96 and the new remainder 3, and apply the division lemma to get
96 = 3 x 32 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 681 and 2238 is 3
Notice that 3 = HCF(96,3) = HCF(195,96) = HCF(681,195) = HCF(2238,681) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8284 > 3, we apply the division lemma to 8284 and 3, to get
8284 = 3 x 2761 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 8284 is 1
Notice that 1 = HCF(3,1) = HCF(8284,3) .
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Frequently Asked Questions on HCF of 681, 2238, 8284 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 681, 2238, 8284?
Answer: HCF of 681, 2238, 8284 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 681, 2238, 8284 using Euclid's Algorithm?
Answer: For arbitrary numbers 681, 2238, 8284 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.