Highest Common Factor of 206, 704, 893 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 206, 704, 893 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 206, 704, 893 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 206, 704, 893 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 206, 704, 893 is 1.

HCF(206, 704, 893) = 1

HCF of 206, 704, 893 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 206, 704, 893 is 1.

Highest Common Factor of 206,704,893 using Euclid's algorithm

Highest Common Factor of 206,704,893 is 1

Step 1: Since 704 > 206, we apply the division lemma to 704 and 206, to get

704 = 206 x 3 + 86

Step 2: Since the reminder 206 ≠ 0, we apply division lemma to 86 and 206, to get

206 = 86 x 2 + 34

Step 3: We consider the new divisor 86 and the new remainder 34, and apply the division lemma to get

86 = 34 x 2 + 18

We consider the new divisor 34 and the new remainder 18,and apply the division lemma to get

34 = 18 x 1 + 16

We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get

18 = 16 x 1 + 2

We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get

16 = 2 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 206 and 704 is 2

Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(34,18) = HCF(86,34) = HCF(206,86) = HCF(704,206) .

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

Step 1: Since 893 > 2, we apply the division lemma to 893 and 2, to get

893 = 2 x 446 + 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 893 is 1

Notice that 1 = HCF(2,1) = HCF(893,2) .

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Frequently Asked Questions on HCF of 206, 704, 893 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 206, 704, 893?

Answer: HCF of 206, 704, 893 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 206, 704, 893 using Euclid's Algorithm?

Answer: For arbitrary numbers 206, 704, 893 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.