Highest Common Factor of 8514, 6970 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 8514, 6970 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8514, 6970 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 8514, 6970 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 8514, 6970 is 2.
HCF(8514, 6970) = 2
HCF of 8514, 6970 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8514, 6970 is 2.
Highest Common Factor of 8514,6970 is 2
Step 1: Since 8514 > 6970, we apply the division lemma to 8514 and 6970, to get
8514 = 6970 x 1 + 1544
Step 2: Since the reminder 6970 ≠ 0, we apply division lemma to 1544 and 6970, to get
6970 = 1544 x 4 + 794
Step 3: We consider the new divisor 1544 and the new remainder 794, and apply the division lemma to get
1544 = 794 x 1 + 750
We consider the new divisor 794 and the new remainder 750,and apply the division lemma to get
794 = 750 x 1 + 44
We consider the new divisor 750 and the new remainder 44,and apply the division lemma to get
750 = 44 x 17 + 2
We consider the new divisor 44 and the new remainder 2,and apply the division lemma to get
44 = 2 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8514 and 6970 is 2
Notice that 2 = HCF(44,2) = HCF(750,44) = HCF(794,750) = HCF(1544,794) = HCF(6970,1544) = HCF(8514,6970) .
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Frequently Asked Questions on HCF of 8514, 6970 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 8514, 6970?
Answer: HCF of 8514, 6970 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8514, 6970 using Euclid's Algorithm?
Answer: For arbitrary numbers 8514, 6970 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.