Highest Common Factor of 506, 794, 313 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 506, 794, 313 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 506, 794, 313 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 506, 794, 313 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 506, 794, 313 is 1.

HCF(506, 794, 313) = 1

HCF of 506, 794, 313 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 506, 794, 313 is 1.

Highest Common Factor of 506,794,313 using Euclid's algorithm

Highest Common Factor of 506,794,313 is 1

Step 1: Since 794 > 506, we apply the division lemma to 794 and 506, to get

794 = 506 x 1 + 288

Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 288 and 506, to get

506 = 288 x 1 + 218

Step 3: We consider the new divisor 288 and the new remainder 218, and apply the division lemma to get

288 = 218 x 1 + 70

We consider the new divisor 218 and the new remainder 70,and apply the division lemma to get

218 = 70 x 3 + 8

We consider the new divisor 70 and the new remainder 8,and apply the division lemma to get

70 = 8 x 8 + 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 506 and 794 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(70,8) = HCF(218,70) = HCF(288,218) = HCF(506,288) = HCF(794,506) .

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

Step 1: Since 313 > 2, we apply the division lemma to 313 and 2, to get

313 = 2 x 156 + 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 313 is 1

Notice that 1 = HCF(2,1) = HCF(313,2) .

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Frequently Asked Questions on HCF of 506, 794, 313 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 506, 794, 313?

Answer: HCF of 506, 794, 313 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 506, 794, 313 using Euclid's Algorithm?

Answer: For arbitrary numbers 506, 794, 313 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.