Highest Common Factor of 683, 419 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 683, 419 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 683, 419 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 683, 419 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 683, 419 is 1.
HCF(683, 419) = 1
HCF of 683, 419 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 683, 419 is 1.
Highest Common Factor of 683,419 is 1
Step 1: Since 683 > 419, we apply the division lemma to 683 and 419, to get
683 = 419 x 1 + 264
Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 264 and 419, to get
419 = 264 x 1 + 155
Step 3: We consider the new divisor 264 and the new remainder 155, and apply the division lemma to get
264 = 155 x 1 + 109
We consider the new divisor 155 and the new remainder 109,and apply the division lemma to get
155 = 109 x 1 + 46
We consider the new divisor 109 and the new remainder 46,and apply the division lemma to get
109 = 46 x 2 + 17
We consider the new divisor 46 and the new remainder 17,and apply the division lemma to get
46 = 17 x 2 + 12
We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get
17 = 12 x 1 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 683 and 419 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(46,17) = HCF(109,46) = HCF(155,109) = HCF(264,155) = HCF(419,264) = HCF(683,419) .
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Frequently Asked Questions on HCF of 683, 419 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 683, 419?
Answer: HCF of 683, 419 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 683, 419 using Euclid's Algorithm?
Answer: For arbitrary numbers 683, 419 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.