Highest Common Factor of 220, 582, 341 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 220, 582, 341 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 220, 582, 341 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 220, 582, 341 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 220, 582, 341 is 1.
HCF(220, 582, 341) = 1
HCF of 220, 582, 341 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 220, 582, 341 is 1.
Highest Common Factor of 220,582,341 is 1
Step 1: Since 582 > 220, we apply the division lemma to 582 and 220, to get
582 = 220 x 2 + 142
Step 2: Since the reminder 220 ≠ 0, we apply division lemma to 142 and 220, to get
220 = 142 x 1 + 78
Step 3: We consider the new divisor 142 and the new remainder 78, and apply the division lemma to get
142 = 78 x 1 + 64
We consider the new divisor 78 and the new remainder 64,and apply the division lemma to get
78 = 64 x 1 + 14
We consider the new divisor 64 and the new remainder 14,and apply the division lemma to get
64 = 14 x 4 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 220 and 582 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(64,14) = HCF(78,64) = HCF(142,78) = HCF(220,142) = HCF(582,220) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 341 > 2, we apply the division lemma to 341 and 2, to get
341 = 2 x 170 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 341 is 1
Notice that 1 = HCF(2,1) = HCF(341,2) .
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Frequently Asked Questions on HCF of 220, 582, 341 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 220, 582, 341?
Answer: HCF of 220, 582, 341 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 220, 582, 341 using Euclid's Algorithm?
Answer: For arbitrary numbers 220, 582, 341 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
