Highest Common Factor of 434, 313, 817 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 434, 313, 817 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 434, 313, 817 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 434, 313, 817 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 434, 313, 817 is 1.

HCF(434, 313, 817) = 1

HCF of 434, 313, 817 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 434, 313, 817 is 1.

Highest Common Factor of 434,313,817 using Euclid's algorithm

Highest Common Factor of 434,313,817 is 1

Step 1: Since 434 > 313, we apply the division lemma to 434 and 313, to get

434 = 313 x 1 + 121

Step 2: Since the reminder 313 ≠ 0, we apply division lemma to 121 and 313, to get

313 = 121 x 2 + 71

Step 3: We consider the new divisor 121 and the new remainder 71, and apply the division lemma to get

121 = 71 x 1 + 50

We consider the new divisor 71 and the new remainder 50,and apply the division lemma to get

71 = 50 x 1 + 21

We consider the new divisor 50 and the new remainder 21,and apply the division lemma to get

50 = 21 x 2 + 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 434 and 313 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(50,21) = HCF(71,50) = HCF(121,71) = HCF(313,121) = HCF(434,313) .

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

Step 1: Since 817 > 1, we apply the division lemma to 817 and 1, to get

817 = 1 x 817 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 817 is 1

Notice that 1 = HCF(817,1) .

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Frequently Asked Questions on HCF of 434, 313, 817 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 434, 313, 817?

Answer: HCF of 434, 313, 817 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 434, 313, 817 using Euclid's Algorithm?

Answer: For arbitrary numbers 434, 313, 817 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.