Highest Common Factor of 582, 226, 454 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, 226, 454 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 582, 226, 454 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, 226, 454 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, 226, 454 is 2.
HCF(582, 226, 454) = 2
HCF of 582, 226, 454 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, 226, 454 is 2.
Highest Common Factor of 582,226,454 is 2
Step 1: Since 582 > 226, we apply the division lemma to 582 and 226, to get
582 = 226 x 2 + 130
Step 2: Since the reminder 226 ≠ 0, we apply division lemma to 130 and 226, to get
226 = 130 x 1 + 96
Step 3: We consider the new divisor 130 and the new remainder 96, and apply the division lemma to get
130 = 96 x 1 + 34
We consider the new divisor 96 and the new remainder 34,and apply the division lemma to get
96 = 34 x 2 + 28
We consider the new divisor 34 and the new remainder 28,and apply the division lemma to get
34 = 28 x 1 + 6
We consider the new divisor 28 and the new remainder 6,and apply the division lemma to get
28 = 6 x 4 + 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 226 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(28,6) = HCF(34,28) = HCF(96,34) = HCF(130,96) = HCF(226,130) = HCF(582,226) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 454 > 2, we apply the division lemma to 454 and 2, to get
454 = 2 x 227 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 454 is 2
Notice that 2 = HCF(454,2) .
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Frequently Asked Questions on HCF of 582, 226, 454 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, 226, 454?
Answer: HCF of 582, 226, 454 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 582, 226, 454 using Euclid's Algorithm?
Answer: For arbitrary numbers 582, 226, 454 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.