Highest Common Factor of 540, 205, 822 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 540, 205, 822 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 540, 205, 822 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 540, 205, 822 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 540, 205, 822 is 1.

HCF(540, 205, 822) = 1

HCF of 540, 205, 822 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 540, 205, 822 is 1.

Highest Common Factor of 540,205,822 using Euclid's algorithm

Highest Common Factor of 540,205,822 is 1

Step 1: Since 540 > 205, we apply the division lemma to 540 and 205, to get

540 = 205 x 2 + 130

Step 2: Since the reminder 205 ≠ 0, we apply division lemma to 130 and 205, to get

205 = 130 x 1 + 75

Step 3: We consider the new divisor 130 and the new remainder 75, and apply the division lemma to get

130 = 75 x 1 + 55

We consider the new divisor 75 and the new remainder 55,and apply the division lemma to get

75 = 55 x 1 + 20

We consider the new divisor 55 and the new remainder 20,and apply the division lemma to get

55 = 20 x 2 + 15

We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get

20 = 15 x 1 + 5

We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get

15 = 5 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 540 and 205 is 5

Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(55,20) = HCF(75,55) = HCF(130,75) = HCF(205,130) = HCF(540,205) .

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

Step 1: Since 822 > 5, we apply the division lemma to 822 and 5, to get

822 = 5 x 164 + 2

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get

5 = 2 x 2 + 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 5 and 822 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(822,5) .

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Frequently Asked Questions on HCF of 540, 205, 822 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 540, 205, 822?

Answer: HCF of 540, 205, 822 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 540, 205, 822 using Euclid's Algorithm?

Answer: For arbitrary numbers 540, 205, 822 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.