Highest Common Factor of 205, 743, 249 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 205, 743, 249 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 205, 743, 249 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 205, 743, 249 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 205, 743, 249 is 1.

HCF(205, 743, 249) = 1

HCF of 205, 743, 249 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 205, 743, 249 is 1.

Highest Common Factor of 205,743,249 using Euclid's algorithm

Highest Common Factor of 205,743,249 is 1

Step 1: Since 743 > 205, we apply the division lemma to 743 and 205, to get

743 = 205 x 3 + 128

Step 2: Since the reminder 205 ≠ 0, we apply division lemma to 128 and 205, to get

205 = 128 x 1 + 77

Step 3: We consider the new divisor 128 and the new remainder 77, and apply the division lemma to get

128 = 77 x 1 + 51

We consider the new divisor 77 and the new remainder 51,and apply the division lemma to get

77 = 51 x 1 + 26

We consider the new divisor 51 and the new remainder 26,and apply the division lemma to get

51 = 26 x 1 + 25

We consider the new divisor 26 and the new remainder 25,and apply the division lemma to get

26 = 25 x 1 + 1

We consider the new divisor 25 and the new remainder 1,and apply the division lemma to get

25 = 1 x 25 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 205 and 743 is 1

Notice that 1 = HCF(25,1) = HCF(26,25) = HCF(51,26) = HCF(77,51) = HCF(128,77) = HCF(205,128) = HCF(743,205) .

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

Step 1: Since 249 > 1, we apply the division lemma to 249 and 1, to get

249 = 1 x 249 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 249 is 1

Notice that 1 = HCF(249,1) .

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Frequently Asked Questions on HCF of 205, 743, 249 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 205, 743, 249?

Answer: HCF of 205, 743, 249 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 205, 743, 249 using Euclid's Algorithm?

Answer: For arbitrary numbers 205, 743, 249 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.