Highest Common Factor of 814, 353, 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 814, 353, 313 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 814, 353, 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 814, 353, 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 814, 353, 313 is 1.

HCF(814, 353, 313) = 1

HCF of 814, 353, 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 814, 353, 313 is 1.

Highest Common Factor of 814,353,313 using Euclid's algorithm

Highest Common Factor of 814,353,313 is 1

Step 1: Since 814 > 353, we apply the division lemma to 814 and 353, to get

814 = 353 x 2 + 108

Step 2: Since the reminder 353 ≠ 0, we apply division lemma to 108 and 353, to get

353 = 108 x 3 + 29

Step 3: We consider the new divisor 108 and the new remainder 29, and apply the division lemma to get

108 = 29 x 3 + 21

We consider the new divisor 29 and the new remainder 21,and apply the division lemma to get

29 = 21 x 1 + 8

We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get

21 = 8 x 2 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 814 and 353 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(29,21) = HCF(108,29) = HCF(353,108) = HCF(814,353) .

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

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

313 = 1 x 313 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 313 is 1

Notice that 1 = HCF(313,1) .

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Frequently Asked Questions on HCF of 814, 353, 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 814, 353, 313?

Answer: HCF of 814, 353, 313 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 814, 353, 313 using Euclid's Algorithm?

Answer: For arbitrary numbers 814, 353, 313 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.