Highest Common Factor of 913, 586 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 913, 586 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 913, 586 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 913, 586 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 913, 586 is 1.

HCF(913, 586) = 1

HCF of 913, 586 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 913, 586 is 1.

Highest Common Factor of 913,586 using Euclid's algorithm

Highest Common Factor of 913,586 is 1

Step 1: Since 913 > 586, we apply the division lemma to 913 and 586, to get

913 = 586 x 1 + 327

Step 2: Since the reminder 586 ≠ 0, we apply division lemma to 327 and 586, to get

586 = 327 x 1 + 259

Step 3: We consider the new divisor 327 and the new remainder 259, and apply the division lemma to get

327 = 259 x 1 + 68

We consider the new divisor 259 and the new remainder 68,and apply the division lemma to get

259 = 68 x 3 + 55

We consider the new divisor 68 and the new remainder 55,and apply the division lemma to get

68 = 55 x 1 + 13

We consider the new divisor 55 and the new remainder 13,and apply the division lemma to get

55 = 13 x 4 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 913 and 586 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(55,13) = HCF(68,55) = HCF(259,68) = HCF(327,259) = HCF(586,327) = HCF(913,586) .

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Frequently Asked Questions on HCF of 913, 586 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 913, 586?

Answer: HCF of 913, 586 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 913, 586 using Euclid's Algorithm?

Answer: For arbitrary numbers 913, 586 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.