Highest Common Factor of 873, 543, 257 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 873, 543, 257 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 873, 543, 257 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 873, 543, 257 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 873, 543, 257 is 1.

HCF(873, 543, 257) = 1

HCF of 873, 543, 257 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 873, 543, 257 is 1.

Highest Common Factor of 873,543,257 using Euclid's algorithm

Highest Common Factor of 873,543,257 is 1

Step 1: Since 873 > 543, we apply the division lemma to 873 and 543, to get

873 = 543 x 1 + 330

Step 2: Since the reminder 543 ≠ 0, we apply division lemma to 330 and 543, to get

543 = 330 x 1 + 213

Step 3: We consider the new divisor 330 and the new remainder 213, and apply the division lemma to get

330 = 213 x 1 + 117

We consider the new divisor 213 and the new remainder 117,and apply the division lemma to get

213 = 117 x 1 + 96

We consider the new divisor 117 and the new remainder 96,and apply the division lemma to get

117 = 96 x 1 + 21

We consider the new divisor 96 and the new remainder 21,and apply the division lemma to get

96 = 21 x 4 + 12

We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get

21 = 12 x 1 + 9

We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get

12 = 9 x 1 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 873 and 543 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(96,21) = HCF(117,96) = HCF(213,117) = HCF(330,213) = HCF(543,330) = HCF(873,543) .

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

Step 1: Since 257 > 3, we apply the division lemma to 257 and 3, to get

257 = 3 x 85 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 257 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(257,3) .

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Frequently Asked Questions on HCF of 873, 543, 257 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 873, 543, 257?

Answer: HCF of 873, 543, 257 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 873, 543, 257 using Euclid's Algorithm?

Answer: For arbitrary numbers 873, 543, 257 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.