Highest Common Factor of 711, 983, 205 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 711, 983, 205 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 711, 983, 205 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 711, 983, 205 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 711, 983, 205 is 1.

HCF(711, 983, 205) = 1

HCF of 711, 983, 205 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 711, 983, 205 is 1.

Highest Common Factor of 711,983,205 using Euclid's algorithm

Highest Common Factor of 711,983,205 is 1

Step 1: Since 983 > 711, we apply the division lemma to 983 and 711, to get

983 = 711 x 1 + 272

Step 2: Since the reminder 711 ≠ 0, we apply division lemma to 272 and 711, to get

711 = 272 x 2 + 167

Step 3: We consider the new divisor 272 and the new remainder 167, and apply the division lemma to get

272 = 167 x 1 + 105

We consider the new divisor 167 and the new remainder 105,and apply the division lemma to get

167 = 105 x 1 + 62

We consider the new divisor 105 and the new remainder 62,and apply the division lemma to get

105 = 62 x 1 + 43

We consider the new divisor 62 and the new remainder 43,and apply the division lemma to get

62 = 43 x 1 + 19

We consider the new divisor 43 and the new remainder 19,and apply the division lemma to get

43 = 19 x 2 + 5

We consider the new divisor 19 and the new remainder 5,and apply the division lemma to get

19 = 5 x 3 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 711 and 983 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(43,19) = HCF(62,43) = HCF(105,62) = HCF(167,105) = HCF(272,167) = HCF(711,272) = HCF(983,711) .

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

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

205 = 1 x 205 + 0

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

Notice that 1 = HCF(205,1) .

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Frequently Asked Questions on HCF of 711, 983, 205 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 711, 983, 205?

Answer: HCF of 711, 983, 205 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 711, 983, 205 using Euclid's Algorithm?

Answer: For arbitrary numbers 711, 983, 205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.