Highest Common Factor of 580, 5420, 8405 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, 5420, 8405 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 580, 5420, 8405 is 5 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, 5420, 8405 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, 5420, 8405 is 5.
HCF(580, 5420, 8405) = 5
HCF of 580, 5420, 8405 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, 5420, 8405 is 5.
Highest Common Factor of 580,5420,8405 is 5
Step 1: Since 5420 > 580, we apply the division lemma to 5420 and 580, to get
5420 = 580 x 9 + 200
Step 2: Since the reminder 580 ≠ 0, we apply division lemma to 200 and 580, to get
580 = 200 x 2 + 180
Step 3: We consider the new divisor 200 and the new remainder 180, and apply the division lemma to get
200 = 180 x 1 + 20
We consider the new divisor 180 and the new remainder 20, and apply the division lemma to get
180 = 20 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 580 and 5420 is 20
Notice that 20 = HCF(180,20) = HCF(200,180) = HCF(580,200) = HCF(5420,580) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8405 > 20, we apply the division lemma to 8405 and 20, to get
8405 = 20 x 420 + 5
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 5 and 20, to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 20 and 8405 is 5
Notice that 5 = HCF(20,5) = HCF(8405,20) .
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Frequently Asked Questions on HCF of 580, 5420, 8405 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, 5420, 8405?
Answer: HCF of 580, 5420, 8405 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 580, 5420, 8405 using Euclid's Algorithm?
Answer: For arbitrary numbers 580, 5420, 8405 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.