Highest Common Factor of 657, 239, 413 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 657, 239, 413 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 657, 239, 413 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 657, 239, 413 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 657, 239, 413 is 1.
HCF(657, 239, 413) = 1
HCF of 657, 239, 413 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 657, 239, 413 is 1.
Highest Common Factor of 657,239,413 is 1
Step 1: Since 657 > 239, we apply the division lemma to 657 and 239, to get
657 = 239 x 2 + 179
Step 2: Since the reminder 239 ≠ 0, we apply division lemma to 179 and 239, to get
239 = 179 x 1 + 60
Step 3: We consider the new divisor 179 and the new remainder 60, and apply the division lemma to get
179 = 60 x 2 + 59
We consider the new divisor 60 and the new remainder 59,and apply the division lemma to get
60 = 59 x 1 + 1
We consider the new divisor 59 and the new remainder 1,and apply the division lemma to get
59 = 1 x 59 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 657 and 239 is 1
Notice that 1 = HCF(59,1) = HCF(60,59) = HCF(179,60) = HCF(239,179) = HCF(657,239) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 413 > 1, we apply the division lemma to 413 and 1, to get
413 = 1 x 413 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 413 is 1
Notice that 1 = HCF(413,1) .
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Frequently Asked Questions on HCF of 657, 239, 413 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 657, 239, 413?
Answer: HCF of 657, 239, 413 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 657, 239, 413 using Euclid's Algorithm?
Answer: For arbitrary numbers 657, 239, 413 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.