Highest Common Factor of 709, 8097 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 709, 8097 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 709, 8097 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 709, 8097 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 709, 8097 is 1.
HCF(709, 8097) = 1
HCF of 709, 8097 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 709, 8097 is 1.
Highest Common Factor of 709,8097 is 1
Step 1: Since 8097 > 709, we apply the division lemma to 8097 and 709, to get
8097 = 709 x 11 + 298
Step 2: Since the reminder 709 ≠ 0, we apply division lemma to 298 and 709, to get
709 = 298 x 2 + 113
Step 3: We consider the new divisor 298 and the new remainder 113, and apply the division lemma to get
298 = 113 x 2 + 72
We consider the new divisor 113 and the new remainder 72,and apply the division lemma to get
113 = 72 x 1 + 41
We consider the new divisor 72 and the new remainder 41,and apply the division lemma to get
72 = 41 x 1 + 31
We consider the new divisor 41 and the new remainder 31,and apply the division lemma to get
41 = 31 x 1 + 10
We consider the new divisor 31 and the new remainder 10,and apply the division lemma to get
31 = 10 x 3 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 709 and 8097 is 1
Notice that 1 = HCF(10,1) = HCF(31,10) = HCF(41,31) = HCF(72,41) = HCF(113,72) = HCF(298,113) = HCF(709,298) = HCF(8097,709) .
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Frequently Asked Questions on HCF of 709, 8097 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 709, 8097?
Answer: HCF of 709, 8097 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 709, 8097 using Euclid's Algorithm?
Answer: For arbitrary numbers 709, 8097 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.