Highest Common Factor of 6854, 8298 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 6854, 8298 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6854, 8298 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 6854, 8298 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 6854, 8298 is 2.
HCF(6854, 8298) = 2
HCF of 6854, 8298 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6854, 8298 is 2.
Highest Common Factor of 6854,8298 is 2
Step 1: Since 8298 > 6854, we apply the division lemma to 8298 and 6854, to get
8298 = 6854 x 1 + 1444
Step 2: Since the reminder 6854 ≠ 0, we apply division lemma to 1444 and 6854, to get
6854 = 1444 x 4 + 1078
Step 3: We consider the new divisor 1444 and the new remainder 1078, and apply the division lemma to get
1444 = 1078 x 1 + 366
We consider the new divisor 1078 and the new remainder 366,and apply the division lemma to get
1078 = 366 x 2 + 346
We consider the new divisor 366 and the new remainder 346,and apply the division lemma to get
366 = 346 x 1 + 20
We consider the new divisor 346 and the new remainder 20,and apply the division lemma to get
346 = 20 x 17 + 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 6854 and 8298 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(346,20) = HCF(366,346) = HCF(1078,366) = HCF(1444,1078) = HCF(6854,1444) = HCF(8298,6854) .
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Frequently Asked Questions on HCF of 6854, 8298 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 6854, 8298?
Answer: HCF of 6854, 8298 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6854, 8298 using Euclid's Algorithm?
Answer: For arbitrary numbers 6854, 8298 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
