Highest Common Factor of 517, 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 517, 658 i.e. 47 the largest integer that leaves a remainder zero for all numbers.
HCF of 517, 658 is 47 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 517, 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 517, 658 is 47.
HCF(517, 658) = 47
HCF of 517, 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 517, 658 is 47.
Highest Common Factor of 517,658 is 47
Step 1: Since 658 > 517, we apply the division lemma to 658 and 517, to get
658 = 517 x 1 + 141
Step 2: Since the reminder 517 ≠ 0, we apply division lemma to 141 and 517, to get
517 = 141 x 3 + 94
Step 3: We consider the new divisor 141 and the new remainder 94, and apply the division lemma to get
141 = 94 x 1 + 47
We consider the new divisor 94 and the new remainder 47, and apply the division lemma to get
94 = 47 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 47, the HCF of 517 and 658 is 47
Notice that 47 = HCF(94,47) = HCF(141,94) = HCF(517,141) = HCF(658,517) .
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Frequently Asked Questions on HCF of 517, 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 517, 658?
Answer: HCF of 517, 658 is 47 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 517, 658 using Euclid's Algorithm?
Answer: For arbitrary numbers 517, 658 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
