Highest Common Factor of 686, 407, 344 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, 407, 344 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 686, 407, 344 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, 407, 344 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, 407, 344 is 1.
HCF(686, 407, 344) = 1
HCF of 686, 407, 344 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, 407, 344 is 1.
Highest Common Factor of 686,407,344 is 1
Step 1: Since 686 > 407, we apply the division lemma to 686 and 407, to get
686 = 407 x 1 + 279
Step 2: Since the reminder 407 ≠ 0, we apply division lemma to 279 and 407, to get
407 = 279 x 1 + 128
Step 3: We consider the new divisor 279 and the new remainder 128, and apply the division lemma to get
279 = 128 x 2 + 23
We consider the new divisor 128 and the new remainder 23,and apply the division lemma to get
128 = 23 x 5 + 13
We consider the new divisor 23 and the new remainder 13,and apply the division lemma to get
23 = 13 x 1 + 10
We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get
13 = 10 x 1 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 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 686 and 407 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(23,13) = HCF(128,23) = HCF(279,128) = HCF(407,279) = HCF(686,407) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 344 > 1, we apply the division lemma to 344 and 1, to get
344 = 1 x 344 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 344 is 1
Notice that 1 = HCF(344,1) .
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Frequently Asked Questions on HCF of 686, 407, 344 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, 407, 344?
Answer: HCF of 686, 407, 344 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 686, 407, 344 using Euclid's Algorithm?
Answer: For arbitrary numbers 686, 407, 344 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.