Highest Common Factor of 6712, 8200 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 6712, 8200 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 6712, 8200 is 8 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 6712, 8200 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 6712, 8200 is 8.
HCF(6712, 8200) = 8
HCF of 6712, 8200 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6712, 8200 is 8.
Highest Common Factor of 6712,8200 is 8
Step 1: Since 8200 > 6712, we apply the division lemma to 8200 and 6712, to get
8200 = 6712 x 1 + 1488
Step 2: Since the reminder 6712 ≠ 0, we apply division lemma to 1488 and 6712, to get
6712 = 1488 x 4 + 760
Step 3: We consider the new divisor 1488 and the new remainder 760, and apply the division lemma to get
1488 = 760 x 1 + 728
We consider the new divisor 760 and the new remainder 728,and apply the division lemma to get
760 = 728 x 1 + 32
We consider the new divisor 728 and the new remainder 32,and apply the division lemma to get
728 = 32 x 22 + 24
We consider the new divisor 32 and the new remainder 24,and apply the division lemma to get
32 = 24 x 1 + 8
We consider the new divisor 24 and the new remainder 8,and apply the division lemma to get
24 = 8 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 6712 and 8200 is 8
Notice that 8 = HCF(24,8) = HCF(32,24) = HCF(728,32) = HCF(760,728) = HCF(1488,760) = HCF(6712,1488) = HCF(8200,6712) .
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Frequently Asked Questions on HCF of 6712, 8200 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 6712, 8200?
Answer: HCF of 6712, 8200 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6712, 8200 using Euclid's Algorithm?
Answer: For arbitrary numbers 6712, 8200 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.