Highest Common Factor of 422, 5735 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 422, 5735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 422, 5735 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 422, 5735 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 422, 5735 is 1.

HCF(422, 5735) = 1

HCF of 422, 5735 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 422, 5735 is 1.

Highest Common Factor of 422,5735 using Euclid's algorithm

Highest Common Factor of 422,5735 is 1

Step 1: Since 5735 > 422, we apply the division lemma to 5735 and 422, to get

5735 = 422 x 13 + 249

Step 2: Since the reminder 422 ≠ 0, we apply division lemma to 249 and 422, to get

422 = 249 x 1 + 173

Step 3: We consider the new divisor 249 and the new remainder 173, and apply the division lemma to get

249 = 173 x 1 + 76

We consider the new divisor 173 and the new remainder 76,and apply the division lemma to get

173 = 76 x 2 + 21

We consider the new divisor 76 and the new remainder 21,and apply the division lemma to get

76 = 21 x 3 + 13

We consider the new divisor 21 and the new remainder 13,and apply the division lemma to get

21 = 13 x 1 + 8

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 422 and 5735 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(21,13) = HCF(76,21) = HCF(173,76) = HCF(249,173) = HCF(422,249) = HCF(5735,422) .

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Frequently Asked Questions on HCF of 422, 5735 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 422, 5735?

Answer: HCF of 422, 5735 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 422, 5735 using Euclid's Algorithm?

Answer: For arbitrary numbers 422, 5735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.