Highest Common Factor of 882, 543, 428 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 882, 543, 428 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 882, 543, 428 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 882, 543, 428 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 882, 543, 428 is 1.

HCF(882, 543, 428) = 1

HCF of 882, 543, 428 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 882, 543, 428 is 1.

Highest Common Factor of 882,543,428 using Euclid's algorithm

Highest Common Factor of 882,543,428 is 1

Step 1: Since 882 > 543, we apply the division lemma to 882 and 543, to get

882 = 543 x 1 + 339

Step 2: Since the reminder 543 ≠ 0, we apply division lemma to 339 and 543, to get

543 = 339 x 1 + 204

Step 3: We consider the new divisor 339 and the new remainder 204, and apply the division lemma to get

339 = 204 x 1 + 135

We consider the new divisor 204 and the new remainder 135,and apply the division lemma to get

204 = 135 x 1 + 69

We consider the new divisor 135 and the new remainder 69,and apply the division lemma to get

135 = 69 x 1 + 66

We consider the new divisor 69 and the new remainder 66,and apply the division lemma to get

69 = 66 x 1 + 3

We consider the new divisor 66 and the new remainder 3,and apply the division lemma to get

66 = 3 x 22 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 882 and 543 is 3

Notice that 3 = HCF(66,3) = HCF(69,66) = HCF(135,69) = HCF(204,135) = HCF(339,204) = HCF(543,339) = HCF(882,543) .

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

Step 1: Since 428 > 3, we apply the division lemma to 428 and 3, to get

428 = 3 x 142 + 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 428 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(428,3) .

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Frequently Asked Questions on HCF of 882, 543, 428 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 882, 543, 428?

Answer: HCF of 882, 543, 428 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 882, 543, 428 using Euclid's Algorithm?

Answer: For arbitrary numbers 882, 543, 428 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.