Highest Common Factor of 282, 817 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 282, 817 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 282, 817 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 282, 817 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 282, 817 is 1.

HCF(282, 817) = 1

HCF of 282, 817 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 282, 817 is 1.

Highest Common Factor of 282,817 using Euclid's algorithm

Highest Common Factor of 282,817 is 1

Step 1: Since 817 > 282, we apply the division lemma to 817 and 282, to get

817 = 282 x 2 + 253

Step 2: Since the reminder 282 ≠ 0, we apply division lemma to 253 and 282, to get

282 = 253 x 1 + 29

Step 3: We consider the new divisor 253 and the new remainder 29, and apply the division lemma to get

253 = 29 x 8 + 21

We consider the new divisor 29 and the new remainder 21,and apply the division lemma to get

29 = 21 x 1 + 8

We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get

21 = 8 x 2 + 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 282 and 817 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(29,21) = HCF(253,29) = HCF(282,253) = HCF(817,282) .

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Frequently Asked Questions on HCF of 282, 817 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 282, 817?

Answer: HCF of 282, 817 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 282, 817 using Euclid's Algorithm?

Answer: For arbitrary numbers 282, 817 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.