Highest Common Factor of 826, 298, 563 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 826, 298, 563 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 826, 298, 563 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 826, 298, 563 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 826, 298, 563 is 1.

HCF(826, 298, 563) = 1

HCF of 826, 298, 563 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 826, 298, 563 is 1.

Highest Common Factor of 826,298,563 using Euclid's algorithm

Highest Common Factor of 826,298,563 is 1

Step 1: Since 826 > 298, we apply the division lemma to 826 and 298, to get

826 = 298 x 2 + 230

Step 2: Since the reminder 298 ≠ 0, we apply division lemma to 230 and 298, to get

298 = 230 x 1 + 68

Step 3: We consider the new divisor 230 and the new remainder 68, and apply the division lemma to get

230 = 68 x 3 + 26

We consider the new divisor 68 and the new remainder 26,and apply the division lemma to get

68 = 26 x 2 + 16

We consider the new divisor 26 and the new remainder 16,and apply the division lemma to get

26 = 16 x 1 + 10

We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get

16 = 10 x 1 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 826 and 298 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(26,16) = HCF(68,26) = HCF(230,68) = HCF(298,230) = HCF(826,298) .

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

Step 1: Since 563 > 2, we apply the division lemma to 563 and 2, to get

563 = 2 x 281 + 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 563 is 1

Notice that 1 = HCF(2,1) = HCF(563,2) .

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Frequently Asked Questions on HCF of 826, 298, 563 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 826, 298, 563?

Answer: HCF of 826, 298, 563 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 826, 298, 563 using Euclid's Algorithm?

Answer: For arbitrary numbers 826, 298, 563 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.