Highest Common Factor of 419, 658 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 419, 658 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 419, 658 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 419, 658 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 419, 658 is 1.
HCF(419, 658) = 1
HCF of 419, 658 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 419, 658 is 1.
Highest Common Factor of 419,658 is 1
Step 1: Since 658 > 419, we apply the division lemma to 658 and 419, to get
658 = 419 x 1 + 239
Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 239 and 419, to get
419 = 239 x 1 + 180
Step 3: We consider the new divisor 239 and the new remainder 180, and apply the division lemma to get
239 = 180 x 1 + 59
We consider the new divisor 180 and the new remainder 59,and apply the division lemma to get
180 = 59 x 3 + 3
We consider the new divisor 59 and the new remainder 3,and apply the division lemma to get
59 = 3 x 19 + 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 419 and 658 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(59,3) = HCF(180,59) = HCF(239,180) = HCF(419,239) = HCF(658,419) .
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Frequently Asked Questions on HCF of 419, 658 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 419, 658?
Answer: HCF of 419, 658 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 419, 658 using Euclid's Algorithm?
Answer: For arbitrary numbers 419, 658 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.