Highest Common Factor of 686, 4405 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 686, 4405 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 686, 4405 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 686, 4405 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 686, 4405 is 1.
HCF(686, 4405) = 1
HCF of 686, 4405 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 686, 4405 is 1.
Highest Common Factor of 686,4405 is 1
Step 1: Since 4405 > 686, we apply the division lemma to 4405 and 686, to get
4405 = 686 x 6 + 289
Step 2: Since the reminder 686 ≠ 0, we apply division lemma to 289 and 686, to get
686 = 289 x 2 + 108
Step 3: We consider the new divisor 289 and the new remainder 108, and apply the division lemma to get
289 = 108 x 2 + 73
We consider the new divisor 108 and the new remainder 73,and apply the division lemma to get
108 = 73 x 1 + 35
We consider the new divisor 73 and the new remainder 35,and apply the division lemma to get
73 = 35 x 2 + 3
We consider the new divisor 35 and the new remainder 3,and apply the division lemma to get
35 = 3 x 11 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 686 and 4405 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(35,3) = HCF(73,35) = HCF(108,73) = HCF(289,108) = HCF(686,289) = HCF(4405,686) .
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Frequently Asked Questions on HCF of 686, 4405 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 686, 4405?
Answer: HCF of 686, 4405 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 686, 4405 using Euclid's Algorithm?
Answer: For arbitrary numbers 686, 4405 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.