Highest Common Factor of 205, 998, 231 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, 998, 231 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 205, 998, 231 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, 998, 231 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, 998, 231 is 1.

HCF(205, 998, 231) = 1

HCF of 205, 998, 231 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, 998, 231 is 1.

Highest Common Factor of 205,998,231 using Euclid's algorithm

Highest Common Factor of 205,998,231 is 1

Step 1: Since 998 > 205, we apply the division lemma to 998 and 205, to get

998 = 205 x 4 + 178

Step 2: Since the reminder 205 ≠ 0, we apply division lemma to 178 and 205, to get

205 = 178 x 1 + 27

Step 3: We consider the new divisor 178 and the new remainder 27, and apply the division lemma to get

178 = 27 x 6 + 16

We consider the new divisor 27 and the new remainder 16,and apply the division lemma to get

27 = 16 x 1 + 11

We consider the new divisor 16 and the new remainder 11,and apply the division lemma to get

16 = 11 x 1 + 5

We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get

11 = 5 x 2 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 205 and 998 is 1

Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(27,16) = HCF(178,27) = HCF(205,178) = HCF(998,205) .

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

Step 1: Since 231 > 1, we apply the division lemma to 231 and 1, to get

231 = 1 x 231 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 231 is 1

Notice that 1 = HCF(231,1) .

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Frequently Asked Questions on HCF of 205, 998, 231 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, 998, 231?

Answer: HCF of 205, 998, 231 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 205, 998, 231 using Euclid's Algorithm?

Answer: For arbitrary numbers 205, 998, 231 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.