Highest Common Factor of 575, 8421 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 575, 8421 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 575, 8421 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 575, 8421 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 575, 8421 is 1.

HCF(575, 8421) = 1

HCF of 575, 8421 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 575, 8421 is 1.

Highest Common Factor of 575,8421 using Euclid's algorithm

Highest Common Factor of 575,8421 is 1

Step 1: Since 8421 > 575, we apply the division lemma to 8421 and 575, to get

8421 = 575 x 14 + 371

Step 2: Since the reminder 575 ≠ 0, we apply division lemma to 371 and 575, to get

575 = 371 x 1 + 204

Step 3: We consider the new divisor 371 and the new remainder 204, and apply the division lemma to get

371 = 204 x 1 + 167

We consider the new divisor 204 and the new remainder 167,and apply the division lemma to get

204 = 167 x 1 + 37

We consider the new divisor 167 and the new remainder 37,and apply the division lemma to get

167 = 37 x 4 + 19

We consider the new divisor 37 and the new remainder 19,and apply the division lemma to get

37 = 19 x 1 + 18

We consider the new divisor 19 and the new remainder 18,and apply the division lemma to get

19 = 18 x 1 + 1

We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get

18 = 1 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 575 and 8421 is 1

Notice that 1 = HCF(18,1) = HCF(19,18) = HCF(37,19) = HCF(167,37) = HCF(204,167) = HCF(371,204) = HCF(575,371) = HCF(8421,575) .

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Frequently Asked Questions on HCF of 575, 8421 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 575, 8421?

Answer: HCF of 575, 8421 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 575, 8421 using Euclid's Algorithm?

Answer: For arbitrary numbers 575, 8421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.