Highest Common Factor of 203, 289 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 203, 289 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 203, 289 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 203, 289 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 203, 289 is 1.

HCF(203, 289) = 1

HCF of 203, 289 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 203, 289 is 1.

Highest Common Factor of 203,289 using Euclid's algorithm

Highest Common Factor of 203,289 is 1

Step 1: Since 289 > 203, we apply the division lemma to 289 and 203, to get

289 = 203 x 1 + 86

Step 2: Since the reminder 203 ≠ 0, we apply division lemma to 86 and 203, to get

203 = 86 x 2 + 31

Step 3: We consider the new divisor 86 and the new remainder 31, and apply the division lemma to get

86 = 31 x 2 + 24

We consider the new divisor 31 and the new remainder 24,and apply the division lemma to get

31 = 24 x 1 + 7

We consider the new divisor 24 and the new remainder 7,and apply the division lemma to get

24 = 7 x 3 + 3

We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get

7 = 3 x 2 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 203 and 289 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(24,7) = HCF(31,24) = HCF(86,31) = HCF(203,86) = HCF(289,203) .

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Frequently Asked Questions on HCF of 203, 289 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 203, 289?

Answer: HCF of 203, 289 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 203, 289 using Euclid's Algorithm?

Answer: For arbitrary numbers 203, 289 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.