Highest Common Factor of 8512, 6977 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 8512, 6977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8512, 6977 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 8512, 6977 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 8512, 6977 is 1.
HCF(8512, 6977) = 1
HCF of 8512, 6977 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8512, 6977 is 1.
Highest Common Factor of 8512,6977 is 1
Step 1: Since 8512 > 6977, we apply the division lemma to 8512 and 6977, to get
8512 = 6977 x 1 + 1535
Step 2: Since the reminder 6977 ≠ 0, we apply division lemma to 1535 and 6977, to get
6977 = 1535 x 4 + 837
Step 3: We consider the new divisor 1535 and the new remainder 837, and apply the division lemma to get
1535 = 837 x 1 + 698
We consider the new divisor 837 and the new remainder 698,and apply the division lemma to get
837 = 698 x 1 + 139
We consider the new divisor 698 and the new remainder 139,and apply the division lemma to get
698 = 139 x 5 + 3
We consider the new divisor 139 and the new remainder 3,and apply the division lemma to get
139 = 3 x 46 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 8512 and 6977 is 1
Notice that 1 = HCF(3,1) = HCF(139,3) = HCF(698,139) = HCF(837,698) = HCF(1535,837) = HCF(6977,1535) = HCF(8512,6977) .
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Frequently Asked Questions on HCF of 8512, 6977 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 8512, 6977?
Answer: HCF of 8512, 6977 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8512, 6977 using Euclid's Algorithm?
Answer: For arbitrary numbers 8512, 6977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
