Highest Common Factor of 810, 469, 205 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 810, 469, 205 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 810, 469, 205 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 810, 469, 205 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 810, 469, 205 is 1.

HCF(810, 469, 205) = 1

HCF of 810, 469, 205 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 810, 469, 205 is 1.

Highest Common Factor of 810,469,205 using Euclid's algorithm

Highest Common Factor of 810,469,205 is 1

Step 1: Since 810 > 469, we apply the division lemma to 810 and 469, to get

810 = 469 x 1 + 341

Step 2: Since the reminder 469 ≠ 0, we apply division lemma to 341 and 469, to get

469 = 341 x 1 + 128

Step 3: We consider the new divisor 341 and the new remainder 128, and apply the division lemma to get

341 = 128 x 2 + 85

We consider the new divisor 128 and the new remainder 85,and apply the division lemma to get

128 = 85 x 1 + 43

We consider the new divisor 85 and the new remainder 43,and apply the division lemma to get

85 = 43 x 1 + 42

We consider the new divisor 43 and the new remainder 42,and apply the division lemma to get

43 = 42 x 1 + 1

We consider the new divisor 42 and the new remainder 1,and apply the division lemma to get

42 = 1 x 42 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 810 and 469 is 1

Notice that 1 = HCF(42,1) = HCF(43,42) = HCF(85,43) = HCF(128,85) = HCF(341,128) = HCF(469,341) = HCF(810,469) .

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

Step 1: Since 205 > 1, we apply the division lemma to 205 and 1, to get

205 = 1 x 205 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 205 is 1

Notice that 1 = HCF(205,1) .

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Frequently Asked Questions on HCF of 810, 469, 205 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 810, 469, 205?

Answer: HCF of 810, 469, 205 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 810, 469, 205 using Euclid's Algorithm?

Answer: For arbitrary numbers 810, 469, 205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.