Highest Common Factor of 905, 511, 823 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 905, 511, 823 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 905, 511, 823 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 905, 511, 823 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 905, 511, 823 is 1.

HCF(905, 511, 823) = 1

HCF of 905, 511, 823 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 905, 511, 823 is 1.

Highest Common Factor of 905,511,823 using Euclid's algorithm

Highest Common Factor of 905,511,823 is 1

Step 1: Since 905 > 511, we apply the division lemma to 905 and 511, to get

905 = 511 x 1 + 394

Step 2: Since the reminder 511 ≠ 0, we apply division lemma to 394 and 511, to get

511 = 394 x 1 + 117

Step 3: We consider the new divisor 394 and the new remainder 117, and apply the division lemma to get

394 = 117 x 3 + 43

We consider the new divisor 117 and the new remainder 43,and apply the division lemma to get

117 = 43 x 2 + 31

We consider the new divisor 43 and the new remainder 31,and apply the division lemma to get

43 = 31 x 1 + 12

We consider the new divisor 31 and the new remainder 12,and apply the division lemma to get

31 = 12 x 2 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 905 and 511 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(31,12) = HCF(43,31) = HCF(117,43) = HCF(394,117) = HCF(511,394) = HCF(905,511) .

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

Step 1: Since 823 > 1, we apply the division lemma to 823 and 1, to get

823 = 1 x 823 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 823 is 1

Notice that 1 = HCF(823,1) .

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Frequently Asked Questions on HCF of 905, 511, 823 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 905, 511, 823?

Answer: HCF of 905, 511, 823 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 905, 511, 823 using Euclid's Algorithm?

Answer: For arbitrary numbers 905, 511, 823 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.