Highest Common Factor of 903, 559, 371 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 903, 559, 371 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 903, 559, 371 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 903, 559, 371 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 903, 559, 371 is 1.

HCF(903, 559, 371) = 1

HCF of 903, 559, 371 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 903, 559, 371 is 1.

Highest Common Factor of 903,559,371 using Euclid's algorithm

Highest Common Factor of 903,559,371 is 1

Step 1: Since 903 > 559, we apply the division lemma to 903 and 559, to get

903 = 559 x 1 + 344

Step 2: Since the reminder 559 ≠ 0, we apply division lemma to 344 and 559, to get

559 = 344 x 1 + 215

Step 3: We consider the new divisor 344 and the new remainder 215, and apply the division lemma to get

344 = 215 x 1 + 129

We consider the new divisor 215 and the new remainder 129,and apply the division lemma to get

215 = 129 x 1 + 86

We consider the new divisor 129 and the new remainder 86,and apply the division lemma to get

129 = 86 x 1 + 43

We consider the new divisor 86 and the new remainder 43,and apply the division lemma to get

86 = 43 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 43, the HCF of 903 and 559 is 43

Notice that 43 = HCF(86,43) = HCF(129,86) = HCF(215,129) = HCF(344,215) = HCF(559,344) = HCF(903,559) .

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

Step 1: Since 371 > 43, we apply the division lemma to 371 and 43, to get

371 = 43 x 8 + 27

Step 2: Since the reminder 43 ≠ 0, we apply division lemma to 27 and 43, to get

43 = 27 x 1 + 16

Step 3: We consider the new divisor 27 and the new remainder 16, and apply the division lemma to get

27 = 16 x 1 + 11

We consider the new divisor 16 and the new remainder 11,and apply the division lemma to get

16 = 11 x 1 + 5

We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get

11 = 5 x 2 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 43 and 371 is 1

Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(27,16) = HCF(43,27) = HCF(371,43) .

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Frequently Asked Questions on HCF of 903, 559, 371 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 903, 559, 371?

Answer: HCF of 903, 559, 371 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 903, 559, 371 using Euclid's Algorithm?

Answer: For arbitrary numbers 903, 559, 371 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.