Highest Common Factor of 543, 855, 352 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 543, 855, 352 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 543, 855, 352 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 543, 855, 352 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 543, 855, 352 is 1.

HCF(543, 855, 352) = 1

HCF of 543, 855, 352 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 543, 855, 352 is 1.

Highest Common Factor of 543,855,352 using Euclid's algorithm

Highest Common Factor of 543,855,352 is 1

Step 1: Since 855 > 543, we apply the division lemma to 855 and 543, to get

855 = 543 x 1 + 312

Step 2: Since the reminder 543 ≠ 0, we apply division lemma to 312 and 543, to get

543 = 312 x 1 + 231

Step 3: We consider the new divisor 312 and the new remainder 231, and apply the division lemma to get

312 = 231 x 1 + 81

We consider the new divisor 231 and the new remainder 81,and apply the division lemma to get

231 = 81 x 2 + 69

We consider the new divisor 81 and the new remainder 69,and apply the division lemma to get

81 = 69 x 1 + 12

We consider the new divisor 69 and the new remainder 12,and apply the division lemma to get

69 = 12 x 5 + 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 543 and 855 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(69,12) = HCF(81,69) = HCF(231,81) = HCF(312,231) = HCF(543,312) = HCF(855,543) .

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

Step 1: Since 352 > 3, we apply the division lemma to 352 and 3, to get

352 = 3 x 117 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 352 is 1

Notice that 1 = HCF(3,1) = HCF(352,3) .

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Frequently Asked Questions on HCF of 543, 855, 352 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 543, 855, 352?

Answer: HCF of 543, 855, 352 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 543, 855, 352 using Euclid's Algorithm?

Answer: For arbitrary numbers 543, 855, 352 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.