Highest Common Factor of 582, 302 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 582, 302 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 582, 302 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 582, 302 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 582, 302 is 2.
HCF(582, 302) = 2
HCF of 582, 302 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 582, 302 is 2.
Highest Common Factor of 582,302 is 2
Step 1: Since 582 > 302, we apply the division lemma to 582 and 302, to get
582 = 302 x 1 + 280
Step 2: Since the reminder 302 ≠ 0, we apply division lemma to 280 and 302, to get
302 = 280 x 1 + 22
Step 3: We consider the new divisor 280 and the new remainder 22, and apply the division lemma to get
280 = 22 x 12 + 16
We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get
22 = 16 x 1 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 582 and 302 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(280,22) = HCF(302,280) = HCF(582,302) .
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Frequently Asked Questions on HCF of 582, 302 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 582, 302?
Answer: HCF of 582, 302 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 582, 302 using Euclid's Algorithm?
Answer: For arbitrary numbers 582, 302 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.