Highest Common Factor of 686, 455, 164, 349 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, 455, 164, 349 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 686, 455, 164, 349 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, 455, 164, 349 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, 455, 164, 349 is 1.
HCF(686, 455, 164, 349) = 1
HCF of 686, 455, 164, 349 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, 455, 164, 349 is 1.
Highest Common Factor of 686,455,164,349 is 1
Step 1: Since 686 > 455, we apply the division lemma to 686 and 455, to get
686 = 455 x 1 + 231
Step 2: Since the reminder 455 ≠ 0, we apply division lemma to 231 and 455, to get
455 = 231 x 1 + 224
Step 3: We consider the new divisor 231 and the new remainder 224, and apply the division lemma to get
231 = 224 x 1 + 7
We consider the new divisor 224 and the new remainder 7, and apply the division lemma to get
224 = 7 x 32 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 686 and 455 is 7
Notice that 7 = HCF(224,7) = HCF(231,224) = HCF(455,231) = HCF(686,455) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 164 > 7, we apply the division lemma to 164 and 7, to get
164 = 7 x 23 + 3
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 3 and 7, to get
7 = 3 x 2 + 1
Step 3: 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 7 and 164 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(164,7) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 349 > 1, we apply the division lemma to 349 and 1, to get
349 = 1 x 349 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 349 is 1
Notice that 1 = HCF(349,1) .
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Frequently Asked Questions on HCF of 686, 455, 164, 349 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, 455, 164, 349?
Answer: HCF of 686, 455, 164, 349 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 686, 455, 164, 349 using Euclid's Algorithm?
Answer: For arbitrary numbers 686, 455, 164, 349 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.