Highest Common Factor of 823, 511, 381 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 823, 511, 381 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 823, 511, 381 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 823, 511, 381 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 823, 511, 381 is 1.

HCF(823, 511, 381) = 1

HCF of 823, 511, 381 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 823, 511, 381 is 1.

Highest Common Factor of 823,511,381 using Euclid's algorithm

Highest Common Factor of 823,511,381 is 1

Step 1: Since 823 > 511, we apply the division lemma to 823 and 511, to get

823 = 511 x 1 + 312

Step 2: Since the reminder 511 ≠ 0, we apply division lemma to 312 and 511, to get

511 = 312 x 1 + 199

Step 3: We consider the new divisor 312 and the new remainder 199, and apply the division lemma to get

312 = 199 x 1 + 113

We consider the new divisor 199 and the new remainder 113,and apply the division lemma to get

199 = 113 x 1 + 86

We consider the new divisor 113 and the new remainder 86,and apply the division lemma to get

113 = 86 x 1 + 27

We consider the new divisor 86 and the new remainder 27,and apply the division lemma to get

86 = 27 x 3 + 5

We consider the new divisor 27 and the new remainder 5,and apply the division lemma to get

27 = 5 x 5 + 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 823 and 511 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(27,5) = HCF(86,27) = HCF(113,86) = HCF(199,113) = HCF(312,199) = HCF(511,312) = HCF(823,511) .

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

Step 1: Since 381 > 1, we apply the division lemma to 381 and 1, to get

381 = 1 x 381 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 381 is 1

Notice that 1 = HCF(381,1) .

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Frequently Asked Questions on HCF of 823, 511, 381 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 823, 511, 381?

Answer: HCF of 823, 511, 381 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 823, 511, 381 using Euclid's Algorithm?

Answer: For arbitrary numbers 823, 511, 381 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.