Highest Common Factor of 687, 8697 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 687, 8697 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 687, 8697 is 3 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 687, 8697 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 687, 8697 is 3.
HCF(687, 8697) = 3
HCF of 687, 8697 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 687, 8697 is 3.
Highest Common Factor of 687,8697 is 3
Step 1: Since 8697 > 687, we apply the division lemma to 8697 and 687, to get
8697 = 687 x 12 + 453
Step 2: Since the reminder 687 ≠ 0, we apply division lemma to 453 and 687, to get
687 = 453 x 1 + 234
Step 3: We consider the new divisor 453 and the new remainder 234, and apply the division lemma to get
453 = 234 x 1 + 219
We consider the new divisor 234 and the new remainder 219,and apply the division lemma to get
234 = 219 x 1 + 15
We consider the new divisor 219 and the new remainder 15,and apply the division lemma to get
219 = 15 x 14 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 687 and 8697 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(219,15) = HCF(234,219) = HCF(453,234) = HCF(687,453) = HCF(8697,687) .
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Frequently Asked Questions on HCF of 687, 8697 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 687, 8697?
Answer: HCF of 687, 8697 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 687, 8697 using Euclid's Algorithm?
Answer: For arbitrary numbers 687, 8697 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.