Highest Common Factor of 580, 458 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 580, 458 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 580, 458 is 2 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 580, 458 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 580, 458 is 2.
HCF(580, 458) = 2
HCF of 580, 458 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 580, 458 is 2.
Highest Common Factor of 580,458 is 2
Step 1: Since 580 > 458, we apply the division lemma to 580 and 458, to get
580 = 458 x 1 + 122
Step 2: Since the reminder 458 ≠ 0, we apply division lemma to 122 and 458, to get
458 = 122 x 3 + 92
Step 3: We consider the new divisor 122 and the new remainder 92, and apply the division lemma to get
122 = 92 x 1 + 30
We consider the new divisor 92 and the new remainder 30,and apply the division lemma to get
92 = 30 x 3 + 2
We consider the new divisor 30 and the new remainder 2,and apply the division lemma to get
30 = 2 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 580 and 458 is 2
Notice that 2 = HCF(30,2) = HCF(92,30) = HCF(122,92) = HCF(458,122) = HCF(580,458) .
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Frequently Asked Questions on HCF of 580, 458 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 580, 458?
Answer: HCF of 580, 458 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 580, 458 using Euclid's Algorithm?
Answer: For arbitrary numbers 580, 458 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.