Highest Common Factor of 586, 293, 745 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 586, 293, 745 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 586, 293, 745 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 586, 293, 745 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 586, 293, 745 is 1.

HCF(586, 293, 745) = 1

HCF of 586, 293, 745 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 586, 293, 745 is 1.

Highest Common Factor of 586,293,745 using Euclid's algorithm

Highest Common Factor of 586,293,745 is 1

Step 1: Since 586 > 293, we apply the division lemma to 586 and 293, to get

586 = 293 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 293, the HCF of 586 and 293 is 293

Notice that 293 = HCF(586,293) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 745 > 293, we apply the division lemma to 745 and 293, to get

745 = 293 x 2 + 159

Step 2: Since the reminder 293 ≠ 0, we apply division lemma to 159 and 293, to get

293 = 159 x 1 + 134

Step 3: We consider the new divisor 159 and the new remainder 134, and apply the division lemma to get

159 = 134 x 1 + 25

We consider the new divisor 134 and the new remainder 25,and apply the division lemma to get

134 = 25 x 5 + 9

We consider the new divisor 25 and the new remainder 9,and apply the division lemma to get

25 = 9 x 2 + 7

We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get

9 = 7 x 1 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 293 and 745 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(25,9) = HCF(134,25) = HCF(159,134) = HCF(293,159) = HCF(745,293) .

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Frequently Asked Questions on HCF of 586, 293, 745 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 586, 293, 745?

Answer: HCF of 586, 293, 745 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 586, 293, 745 using Euclid's Algorithm?

Answer: For arbitrary numbers 586, 293, 745 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.