Highest Common Factor of 580, 230, 716 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, 230, 716 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 580, 230, 716 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, 230, 716 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, 230, 716 is 2.
HCF(580, 230, 716) = 2
HCF of 580, 230, 716 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, 230, 716 is 2.
Highest Common Factor of 580,230,716 is 2
Step 1: Since 580 > 230, we apply the division lemma to 580 and 230, to get
580 = 230 x 2 + 120
Step 2: Since the reminder 230 ≠ 0, we apply division lemma to 120 and 230, to get
230 = 120 x 1 + 110
Step 3: We consider the new divisor 120 and the new remainder 110, and apply the division lemma to get
120 = 110 x 1 + 10
We consider the new divisor 110 and the new remainder 10, and apply the division lemma to get
110 = 10 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 580 and 230 is 10
Notice that 10 = HCF(110,10) = HCF(120,110) = HCF(230,120) = HCF(580,230) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 716 > 10, we apply the division lemma to 716 and 10, to get
716 = 10 x 71 + 6
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 6 and 10, to get
10 = 6 x 1 + 4
Step 3: 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 10 and 716 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(716,10) .
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Frequently Asked Questions on HCF of 580, 230, 716 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, 230, 716?
Answer: HCF of 580, 230, 716 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 580, 230, 716 using Euclid's Algorithm?
Answer: For arbitrary numbers 580, 230, 716 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.