Highest Common Factor of 721, 8517 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 721, 8517 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 721, 8517 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 721, 8517 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 721, 8517 is 1.
HCF(721, 8517) = 1
HCF of 721, 8517 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 721, 8517 is 1.
Highest Common Factor of 721,8517 is 1
Step 1: Since 8517 > 721, we apply the division lemma to 8517 and 721, to get
8517 = 721 x 11 + 586
Step 2: Since the reminder 721 ≠ 0, we apply division lemma to 586 and 721, to get
721 = 586 x 1 + 135
Step 3: We consider the new divisor 586 and the new remainder 135, and apply the division lemma to get
586 = 135 x 4 + 46
We consider the new divisor 135 and the new remainder 46,and apply the division lemma to get
135 = 46 x 2 + 43
We consider the new divisor 46 and the new remainder 43,and apply the division lemma to get
46 = 43 x 1 + 3
We consider the new divisor 43 and the new remainder 3,and apply the division lemma to get
43 = 3 x 14 + 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 721 and 8517 is 1
Notice that 1 = HCF(3,1) = HCF(43,3) = HCF(46,43) = HCF(135,46) = HCF(586,135) = HCF(721,586) = HCF(8517,721) .
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Frequently Asked Questions on HCF of 721, 8517 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 721, 8517?
Answer: HCF of 721, 8517 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 721, 8517 using Euclid's Algorithm?
Answer: For arbitrary numbers 721, 8517 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.