Highest Common Factor of 540, 766, 211 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, 766, 211 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 540, 766, 211 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, 766, 211 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, 766, 211 is 1.

HCF(540, 766, 211) = 1

HCF of 540, 766, 211 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, 766, 211 is 1.

Highest Common Factor of 540,766,211 using Euclid's algorithm

Highest Common Factor of 540,766,211 is 1

Step 1: Since 766 > 540, we apply the division lemma to 766 and 540, to get

766 = 540 x 1 + 226

Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 226 and 540, to get

540 = 226 x 2 + 88

Step 3: We consider the new divisor 226 and the new remainder 88, and apply the division lemma to get

226 = 88 x 2 + 50

We consider the new divisor 88 and the new remainder 50,and apply the division lemma to get

88 = 50 x 1 + 38

We consider the new divisor 50 and the new remainder 38,and apply the division lemma to get

50 = 38 x 1 + 12

We consider the new divisor 38 and the new remainder 12,and apply the division lemma to get

38 = 12 x 3 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 540 and 766 is 2

Notice that 2 = HCF(12,2) = HCF(38,12) = HCF(50,38) = HCF(88,50) = HCF(226,88) = HCF(540,226) = HCF(766,540) .

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

Step 1: Since 211 > 2, we apply the division lemma to 211 and 2, to get

211 = 2 x 105 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 211 is 1

Notice that 1 = HCF(2,1) = HCF(211,2) .

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Frequently Asked Questions on HCF of 540, 766, 211 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, 766, 211?

Answer: HCF of 540, 766, 211 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 540, 766, 211 using Euclid's Algorithm?

Answer: For arbitrary numbers 540, 766, 211 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.