Highest Common Factor of 268, 281 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 268, 281 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 268, 281 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 268, 281 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 268, 281 is 1.

HCF(268, 281) = 1

HCF of 268, 281 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 268, 281 is 1.

Highest Common Factor of 268,281 using Euclid's algorithm

Highest Common Factor of 268,281 is 1

Step 1: Since 281 > 268, we apply the division lemma to 281 and 268, to get

281 = 268 x 1 + 13

Step 2: Since the reminder 268 ≠ 0, we apply division lemma to 13 and 268, to get

268 = 13 x 20 + 8

Step 3: We consider the new divisor 13 and the new remainder 8, and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 268 and 281 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(268,13) = HCF(281,268) .

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Frequently Asked Questions on HCF of 268, 281 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 268, 281?

Answer: HCF of 268, 281 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 268, 281 using Euclid's Algorithm?

Answer: For arbitrary numbers 268, 281 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.