Highest Common Factor of 820, 634, 361 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 820, 634, 361 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 820, 634, 361 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 820, 634, 361 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 820, 634, 361 is 1.

HCF(820, 634, 361) = 1

HCF of 820, 634, 361 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 820, 634, 361 is 1.

Highest Common Factor of 820,634,361 using Euclid's algorithm

Highest Common Factor of 820,634,361 is 1

Step 1: Since 820 > 634, we apply the division lemma to 820 and 634, to get

820 = 634 x 1 + 186

Step 2: Since the reminder 634 ≠ 0, we apply division lemma to 186 and 634, to get

634 = 186 x 3 + 76

Step 3: We consider the new divisor 186 and the new remainder 76, and apply the division lemma to get

186 = 76 x 2 + 34

We consider the new divisor 76 and the new remainder 34,and apply the division lemma to get

76 = 34 x 2 + 8

We consider the new divisor 34 and the new remainder 8,and apply the division lemma to get

34 = 8 x 4 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 820 and 634 is 2

Notice that 2 = HCF(8,2) = HCF(34,8) = HCF(76,34) = HCF(186,76) = HCF(634,186) = HCF(820,634) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 361 > 2, we apply the division lemma to 361 and 2, to get

361 = 2 x 180 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 361 is 1

Notice that 1 = HCF(2,1) = HCF(361,2) .

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Frequently Asked Questions on HCF of 820, 634, 361 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 820, 634, 361?

Answer: HCF of 820, 634, 361 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 820, 634, 361 using Euclid's Algorithm?

Answer: For arbitrary numbers 820, 634, 361 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.