Highest Common Factor of 838, 21181 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 838, 21181 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 838, 21181 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 838, 21181 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 838, 21181 is 1.

HCF(838, 21181) = 1

HCF of 838, 21181 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 838, 21181 is 1.

Highest Common Factor of 838,21181 using Euclid's algorithm

Highest Common Factor of 838,21181 is 1

Step 1: Since 21181 > 838, we apply the division lemma to 21181 and 838, to get

21181 = 838 x 25 + 231

Step 2: Since the reminder 838 ≠ 0, we apply division lemma to 231 and 838, to get

838 = 231 x 3 + 145

Step 3: We consider the new divisor 231 and the new remainder 145, and apply the division lemma to get

231 = 145 x 1 + 86

We consider the new divisor 145 and the new remainder 86,and apply the division lemma to get

145 = 86 x 1 + 59

We consider the new divisor 86 and the new remainder 59,and apply the division lemma to get

86 = 59 x 1 + 27

We consider the new divisor 59 and the new remainder 27,and apply the division lemma to get

59 = 27 x 2 + 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 838 and 21181 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(27,5) = HCF(59,27) = HCF(86,59) = HCF(145,86) = HCF(231,145) = HCF(838,231) = HCF(21181,838) .

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Frequently Asked Questions on HCF of 838, 21181 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 838, 21181?

Answer: HCF of 838, 21181 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 838, 21181 using Euclid's Algorithm?

Answer: For arbitrary numbers 838, 21181 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.