Highest Common Factor of 821, 497 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 821, 497 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 821, 497 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 821, 497 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 821, 497 is 1.

HCF(821, 497) = 1

HCF of 821, 497 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 821, 497 is 1.

Highest Common Factor of 821,497 using Euclid's algorithm

Highest Common Factor of 821,497 is 1

Step 1: Since 821 > 497, we apply the division lemma to 821 and 497, to get

821 = 497 x 1 + 324

Step 2: Since the reminder 497 ≠ 0, we apply division lemma to 324 and 497, to get

497 = 324 x 1 + 173

Step 3: We consider the new divisor 324 and the new remainder 173, and apply the division lemma to get

324 = 173 x 1 + 151

We consider the new divisor 173 and the new remainder 151,and apply the division lemma to get

173 = 151 x 1 + 22

We consider the new divisor 151 and the new remainder 22,and apply the division lemma to get

151 = 22 x 6 + 19

We consider the new divisor 22 and the new remainder 19,and apply the division lemma to get

22 = 19 x 1 + 3

We consider the new divisor 19 and the new remainder 3,and apply the division lemma to get

19 = 3 x 6 + 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 821 and 497 is 1

Notice that 1 = HCF(3,1) = HCF(19,3) = HCF(22,19) = HCF(151,22) = HCF(173,151) = HCF(324,173) = HCF(497,324) = HCF(821,497) .

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Frequently Asked Questions on HCF of 821, 497 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 821, 497?

Answer: HCF of 821, 497 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 821, 497 using Euclid's Algorithm?

Answer: For arbitrary numbers 821, 497 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.